Word+Problems+(Answers)

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 1. Let s represent the smallest number. If this number is even, the other two even numbers must be: (s+2), (s+4) Given: s+(s+2)+(s+4)= 162 3s+6=162 3s/3=156/3 s=52 (s+2)=54 (s+4)=56

Check: 3s+6 |162 For s=52: | 3(52)+6 |162 156+6 |162 162 |162 ∴ LS=RS ✓ Therefore, the three numbers are; s=52, s+2=54, s+4=56. [//kevink2435//]

 2. Let n be the number. Given:

n²-n=6
n²-n-6=0 a=1 Product=ac=-6 b=-1 Sum=-1 c=-6

(n-3)(n+2) ∴ n=3 or n=-2  I've reached this conclusion because if (n-3)(n+2)=0, then one of the factors must be 0. As a result, for (n-3), n must be 3 since 3-3=0. And for (n+2), n must be -2 since -2+2=0.  If the value of n is 3 then: 3²-3=9-3=6. If the value of n is -2, then: (-2)²-(-2)= 4+2=6.  [//kevinku2435//]

 3. Let s represent the number of sets

Given: 16500 sets/ $9500 = 1.74 set/$1

s sets/ 30000 as 1.74 set/$1 ; s=52200

∴ She would sell 52200 TV sets. [//kevink2435//]

<span style="font-family: Verdana,Geneva,sans-serif;"> 4. If x represents the mass of fuel in tonnes from source 1, then Let 1.2x represent the mass of fuel from source 2.

{ To get the minimum cost, the plant must buy fuel that consists of 20% moderate-emission fuel. To get this concentration, the plant must then buy x fuel from source 1 and 1.2x fuel from source 2. }

The value of fuel from source 1 would then be: 6x The value of fuel from source 2 would then be: 7(1.2x)=8.4x

Given: x+1.2x=290 2.2x/2.2=290/2.2 x=131.82

Check: x+1.2x| 290 For x=131.82 131.82+158.18| 290 290 | 290 ∴L.S = R.S ✓

∴ The minimum cost is 6x+8.4x=790.92+1107.29=$1898.21. [//kevink2435//]

<span style="font-family: Verdana,Geneva,sans-serif;"> 5. Let x represent the number of 2-point questions and let y represent the number of 4-point questions on the test. Given: 2x + 4y = 100 ...[1] x + y = 40 ...[2] --> 2x + 2y = 80 ...[3]

[1] - [3]: (2x + 4y) - (2x + 2y) = 100 - 80 2y = 20 y = 10

Substitute y = 10 into [2]: x + y = 40 x + 10 = 40 x = 40 - 10 x = 30

Check: 2x + 4y | 100 For x=10 and y=30: | 2(30) + 4(10) | 100 60 + 40 | 100 100 | 100 L.S = R.S ✓ x + y | 40 For x=10 and y=30: | 10 + 30 | 40 40 | 40 ∴ L.S = R.S ✓ ∴ There are 10 2-point questions and 30 4-point questions on the test. [//a_zhang]//

<span style="font-family: Verdana,Geneva,sans-serif;"> 6. George scored 68% and 75% on two exams. To keep his ipod, he must bring his average up to at least 80%. What must he earn on the third exam?

[N_Anil]

<span style="font-family: Verdana,Geneva,sans-serif;"> 7. Let s represent the smallest number. Let m represent the middle number. Given: s+m+60=3(50) s+m+60=150 s+m=150-60 s+m=90 s=90-m If m<60 and m is an even number, the the lowest possible value for s: s=90-58 s=32 Check: s+m+60 l 150 For s=32, m=58: 32+58+60 l 150 150 l150 ∴L.S = R.S ✓ ∴ The lowest value of the smallest number is s=32. [//kevink2435//]

<span style="font-family: Verdana,Geneva,sans-serif;">

8. Let h represent the total height of the building in metres. Let b represent the height of the building from the summit to the top of Bert's head.

Since the height of the building to Bert's head, the distance from Bert to the building, and the distance from the top of Bert's head to the summit of the building form a triangle, we can apply the Pythagorean Theorem in order to solve this question. Also, since Bert's height is 180 cm, it equals to 1.8 m.

Given: a² + b² = c² 33² + b² = 55² 33² - 33² + b² = 55² - 33² b² = 55² -33² b² = 44² b = 44

Given: h = 1.8 + b h = 1.8 + 44 h = 45.8

Check 1: a² + b² |c² For b=44: 33² + 44² | 55² 1089 + 1936 | 3025 3025 | 3025 ∴ LS = RS √

Check 2:

1.8 + b | h For b = 44 and h = 45.8 1.8 + 44 | 45.8 45.8 | 45.8 ∴ LS = RS √

∴ the height of the building 45.8 m. [//a_zhang//] //__**edited**__// by [kevink2435]
 * __re-edited__** by [vdesai]

<span style="font-family: Verdana,Geneva,sans-serif; display: block; text-align: right;">[kevink2435]

9. Given: First integer is 1/3 × 57= 19 Second integer is 19-5=14

∴ I have proven that this question is impossible to solve because 19 + 14 not= 57

[kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 10. Let b represent the value of the base of the isosceles triangle. Let s represent the length of one of the triangle's equal sides.

given: s = 2b - 3, perimeter = 54 metres

perimeter = long side length + long side length + base length 54 metres = 2s + b 54 metres = 2(2b - 3) + b 54 metres = 4b - 6 + b 60 metres = 5b b = 12 metres s = 2 ×12 - 3 = 21 metres

check: <span style="color: rgb(255, 255, 255);">BLANK 2s + b | 54 for s = 21:<span style="color: rgb(255, 255, 255);">ABC | for b = 12:<span style="color: rgb(255, 255, 255);">ABC | <span style="color: rgb(255, 255, 255);">`~` 2 × 21 + 12 | 54 <span style="color: rgb(255, 255, 255);">`~`~`~` 42 + 12 | 54 <span style="color: rgb(255, 255, 255);">`~`~`~`~`~`~ 54 | 54

∴ RS = LS √ ∴ s = 21, b = 12 ∴ The length of each of the longer sides is 21 metres and the length of the base is 12 metres. [//hli//]

<span style="font-family: Verdana,Geneva,sans-serif;"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);"> 11. <span style="color: rgb(0, 0, 0);">Let h represent the number of hours it takes for the second bus to overtake the first one. a) Given: 80h+40 <100h 40<100h-80h 40/20<20h/20 2<h h>2 Check 80h+40 <100h For h=3: 80(3)+40<100(3) 240+40<300 280<300 ∴ LS<RS -(this is something new!)

∴ Since h>2, the second bus must drive for at least 3 hours. b)<span style="font-family: Verdana,Geneva,sans-serif; color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">∴ The second bus overtook the first at 1:30 P.M.  [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 11. (in //hli//'s point of view) a) <span style="color: rgb(0, 0, 0);">Let h represent the number of hours it takes for the second bus to overtake the first one. <span style="color: rgb(0, 0, 0);"> Given: Bus 1 left at 10 A.M. at the speed of 80 km/h and bus 2 left at 10:30 A.M. at the speed of 100 km/h.

speed of bus 2 × h = speed of bus 1 × h + distance travelled by 10:30 A.M. 100h = 80h + 40 20h = 40 h = 2 hours (after bus 2 left)

check: 100h = 80h + 40 for h=2: 100 (2) | 80 (2) + 40 200 | 160 + 40 <span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;">200 | 200 <span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;">∴ LS = RS √ <span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;">∴ The second bus took 2 hours to overtake the first bus.

b)

<span style="font-family: Verdana,Geneva,sans-serif;"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">∴ The second bus overtook the first bus at 12:30 P.M. <span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);"> <span style="display: block; color: rgb(0, 0, 0); text-align: right;">[//hli]//

12. Let g be the number of green batons. Let y be the number of yellow batons.

Given: The total length of 15 batons is 62 cm and green batons are 3 cm long and yellow batons are 5 cm long.

3g + 5y = 62 g + y = 15

g = 15 - y

3(15 - y) + 5y = 62 45 - 3y + 5y = 62 2y = 17 y = 8.5 (**but you can't have half of 1 baton**)

y = 15 - g

3g + 5(15 - g) = 62 3g + 75 - 5g = 62 -2g = -13 2g = 13 g = 6.5 (//**but you can't have half of 1 baton!!**//)

check: g + y | 15<span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;"> for g=6.5: for y=8.5: 6.5 + <span style="color: rgb(0, 0, 0);">8.5 | 15 15 | 15 <span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;">∴ LS = RS √

check: 3g + 5y | 62 <span style="color: rgb(0, 0, 0);">for g=6.5: for y=8.5: 3(6.5) + 5(8.5) | 62 19.5 + 42.5 | 62 62 | 62 <span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;">∴ LS = RS √ <span style="color: rgb(0, 0, 0); font-family: Verdana,Geneva,sans-serif;">∴ This question has been proven to be impossible to solve because __//**you can NOT have half of 1 baton!!****!!!!**//__ [//hli//]

<span style="font-family: Verdana,Geneva,sans-serif;">13. Given: In total, there are 3+6+5+4=18 parts of the profit ∴ Arash gets 3/18=1/6 of $640000000= $106666666.70 Anthony gets 6/18=1/3 of $640000000=$213333333.3 Anne gets 5/18 of $640000000= $177777777.8 Christina gets 4/18=2/9 of $640000000=$142222222.2 [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 14. There are 100 cm in 1 m. Given: l=(2w-0.5) m P=16 m P=2(l+w) For l=2w-0.5, P=16: 2(2w-0.5+w)=16 2(3w-0.5)=16 6w-1=16 6w/6=17/6 w=2.8 2w-0.5=5.6-0.5=5.1

Check 6w-1 l 16 For w=2.8: 6(2.8)-1 l 16 15.8 l 16 ∴ LS = RS √ (The result is a little off because of rounding.)

If the original dimensions are 2.8 m by 5.1 m, then the new dimensions are:

l=5.1+2(0.5)=6.1 m (There are 2 sides for each dimension, so the original dimensions increase by 2×0.5=1m ) w=2.8+2(0.5)=3.8m

P= 2(l+w) For l=6.1, w=3.8: P=2(6.1+3.8) P=2(9.9) P=19.8 m

Check 2(l+w) l 19.8 For l=6.1, w=3.8: 2(9.9) l 19.8 19.8 l 19.8

∴ LS = RS √

∴ The perimeter is 19.8 m. [//kevink2435//]

<span style="font-family: Verdana,Geneva,sans-serif;"> 15. Let h represent the cost of a hamburger. Let h + 1 represent the cost of a hot dog and let 2h - 2 represent the cost of a sausage.

Given: 5h + 4(h+1) + 4(2h+2) = 30.66 5h + 4h + 4 + 8h + 8 = 30.66 17h + 12 = 30.66 17h = 18.66 h ≈ 1.10

Check: 5h + 4(h+1) + 4(2h+2) | 30.66 For h=1.10: | 5(1.10) + 4(1.10+1) + 4[2(1.10)+2] | 30.66 5.5 + 4.4 + 4 + 8.8 + 8 | 30.66 30.7 | 30.66 ∴L.S ≈ R.S √

∴ The cost of a hamburger is approximately $1.10, the cost of a hot dog is approximately $1.10 + $1 = $2.10, and the cost of a sausage is approximately 2($1.10) - $2 = $1.20 [//a_zhang//]

<span style="font-family: Verdana,Geneva,sans-serif;"> 16. Let p represent how much Kevin was paid in 20 hours.

given: $132 in 9 hours

payment for 1 hour = $132 ÷ 9 total payment = $132 ÷ 9 × 20 = p p = 132 × 20 ÷ 9 <span style="color: rgb(255, 255, 255);">`~ = $293.33

check: 132 × 20 ÷ 9|293.33 <span style="color: rgb(255, 255, 255);">` ~ 2640 ÷ 9|293.33 <span style="color: rgb(255, 255, 255);">~`~` 293.33|293.33 ∴LS = RS √ ∴ Kevin gets paid $293.33 in 20 hours. [//hli//]

17. a) e = 1299 + s ÷ 5, e is the weekly earning for Kevin in dollars and s is the value of Kevin's weekly sales in dollars. b) s = 5 (e - 1299) s = 5 (100 000 000 - 1299) s = 5 (99 998 701) s = 499 993 505

check: 20% of s + 1299 | 100 000 000 for s = 499 993 505: 499 993 505 ÷ 5 + 1299 | 100 000 000 99998701 + 1299 | 100 000 000 100 000 000 | 100 000 000 <span style="font-family: Verdana,Geneva,sans-serif;">∴LS = RS √ ∴The total value of all the shoes that Kevin sold in th at week was $499 993 505. <span style="font-family: Verdana,Geneva,sans-serif; display: block; text-align: right;">[//hli//]

<span style="font-family: Verdana,Geneva,sans-serif;">18. This equation has a partial variation because the dependent variable, V, depends on 3 independent variables:l, w, h.

[kevink2435]

19. Assume that Kevin's journey is in 2 parts. (d = d 1 + d 2 ) Let d be the distance that Kevin travelled. Let t be the time that Kevin took to travel the distance in part 2. Let a be the Kevin's average speed in the second part of his journey.

given: In part 1, Kevin runs at 25 km/h for 5 seconds. In part 2, Kevin decelerates by 2 km/h every 5 seconds.

d 1 = 25 ÷ 3600 × 5 d 2 = a × t a = t = 25 × 5 ÷ 2 = 62.5 seconds

<span style="font-family: Verdana,Geneva,sans-serif; display: block; text-align: right;">[//hli//]
 * PLEASE LEAVE THIS AS IT IS! (__to be continued__)**

<span style="font-family: Verdana,Geneva,sans-serif;"> 20. Let [ ( 32 X 2 ) + S ] be the amount of sunscreen Dude #2 applies. Then the amount of sunscreen applied by Dude #3 is [ ( 32 X 2) ] ÷ 3.

Given: 32 + [ (32 X 2 ) + S] + [ ( 32 X 2 ) ] / 3 = 120

32 + 64 + 64/3 + 2S =120 32 + 64 + 21 +2S = 120 117 + 2S = 120 117- 117 + 2S = 120-117 2S = 3 2S/2 = 3/2 S = 1.5 Therefore S = 2 Check: L.S. R.S. 32 + 64 + 64/3 + 2S I 120 For S = 2: 32 +64 + 64/3 + 2(2) I 120 117 + 4 I 120 120 I 120

Therefore L.S.= R.S. ✓

Therefore Dude #2 [ ( 32 X 2 ) + S ] applied 66 mL and Dude #3 [ ( 32 X 2 ) ] / 3 applied 22 mL of sunscreen.

[Aparischa and h_singh]

21. a) Let j represent the length of Julies' hair. Kim's hair is then (3/4j) cm long

Given: j+ (3/4j)=140 4(j+3/4j)=4(140) 4j+3j=560 7j/7=560/7 j=80 (3/4j)=3/4(80)=60

Check: j+ (3/4j) l 140 For j=80: 80+(3/4×80) l 140 80+60 l 140 140 l 140 <span style="font-family: Verdana,Geneva,sans-serif;">∴LS = RS √ ∴ Julie's hair is 80 cm and Kim's hair is 60 cm. b)∴ The girls would donate (80-5)+(60-5)=75+55=130 cm of hair. [//kevink2435//]

22. Given: l=2w+15 P=60

P=2(l+w) 2(2w+15+w)=60 <span style="font-family: Verdana,Geneva,sans-serif;">2(3w+15)=60 6w+30=60 6w=60-30 6w/6=30/6 w=5 2w+15=25

Check: 2(2w+15+w) l 60 2(5+25) l 60 2(30) l 60 60 l 60 <span style="font-family: Verdana,Geneva,sans-serif;">∴LS = RS √

∴ The length is 2w+15=25 cm and the width is w=5 cm. [//kevink2435//]

23. Let d represent the number of days that Sam works. Given: If Sam earns $12 per hour and works 3 hours per day, then in one day Sam makes $36. 36d/36=252/36 d=7

<span style="font-family: Verdana,Geneva,sans-serif;">∴Sam has to work 7 days in order to earn $252. [//kevink2435//]

24. Let n represent the number.

Given: n² + n³ = 12 --1 ½n² = (3/2) + (1/16)n³ --2

n = 2

Check:

L.S|R.S

for n = 2:

2² +2³ | 12 4 + 8 | 12 12 | 12

½n² | (3/2) + (1/16)n³ ½(2)² | (3/2) + (1/16)(2)³ 2 | (3/2) + (8/16) 2 | 2

.·. L.S = R.S

The two numbers are 4 and 8 [dpan]

25. Given: d=s×t, d is the distance in miles, s is speed in miles/hour, t is time in hours For s=15 and t=3.33: d=15×3.33 d= 49.95=50

∴ The school is about 50 miles apart from his house. [//kevink2435//]

26. Let m represent the height of Marley in real life. There is 10 mm in 1 cm. Given: 2.5/3 as 185/m 2.5m/2.5=555/2.5 m=222

∴ Marley is 222 cm tall in real life [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 27. Let h represent the number of hours that she drove on the highway. Let r represent the number of hours that she drove for the remainder of the trip. She drove 100h km on the highway She drove 90r km for the remainder of trip.

Given: h+r=5; h=5-r.....[1] 100h+90r=470; 100h=470-90r... [2]

100*[1]=[2] 100(5-r)=470-90r 500-100r=470-90r -100r+90r=470-500 -10r=-30 10r/10=30/10 r=3 h=5-r=2

Check: 100h+90r l 470 For h=2, r=3: 100(2)+90(3) l 470 200+270 l 470 470 l 470

∴ LS = RS √ ∴ She drove 100h=200 km at 100km/h and 90r=270 km at 90km/h. [kevink2435]

29. Let a be the speed of Alex. Let r be the total work done on the room. Let f be the speed of the father. Let t be the time it takes the father to paint the room.

Given: 4 (days) × a = r, and: 2 (a+f) = r

4a = r 2 (a+f) = r tf = r 4a = 2a + 2f 2a = 2f 4a = 4f r = 4f tf = 4f t = 4 days

<span style="font-family: Verdana,Geneva,sans-serif;">∴ It takes 4 days for Alex's dad to paint the room by himself. [//hli//]

30. Let t be the time in hours that April took to catch up to Ron.

Given: Ron left at 8 A.M. at a speed of 50 km/h and April left at 10 A.M. at a speed of 70 km/h.

April's speed × t = Ron's speed × t + distance travelled by 10 A.M. 70t = 50t + 100 20t = 100 t = 5 hours (after 10 A.M.)

check: 70t | 50t + 100 for t=5: 70 (5) | 50 (5) + 100 350 | 250 + 100 350 | 350

<span style="font-family: Verdana,Geneva,sans-serif;">∴ LS = RS √ ∴ April passed Ron at 3 P.M. [//hli//]

31. Let m represent the mark that Henry got for the last exam. Given: 9(75)+m=10(90) 675+m= 900 m=900-675 m=225 Check: 9(75)+m l 10(90) 675+m l 900 For m=225: 675+225 l 900 900 l 900 ∴LS = RS √ ∴ Henry got 225% on the last exam and each bonus questions was worth (225-100)/5=125/5=25%. [kevink2435]

33. ∴ The number is 34 [kevink2435]

34. Given: There are 15 balloons along the circumference and the distance between them follows the equation: C=3b+6, b is the number of balloons starting from the first one and C is the circumference. C= 3b+6 For b=15: C=3(15)+6 C=45+6 C=51

Check:

3b+6 l 51 For b=15: 3(15)+6 l 51 45+6 l 51 51 l 51 ∴ LS = RS √

<span style="display: block; font-family: Verdana,Geneva,sans-serif; text-align: left;">∴ The circumference of the circle is C=51 cm.

[kevink2435]

36. Let b be the percentage that Bala got. Let c be the fraction that Bala got, out of 35. Let j be the percentage that Jonathan got. Let k be the fraction that Jonathan got, out of 35. Let d be the fraction that Disha got, out of 22, and let e be the percentage that Disha got.

Given: b=80% j=75% d=20/22

c=(35)(0.80)=28 out of 35 k=(35)(0.75)=26.25 out of 35 e=(20/22)(100)=90%

check: c=(28/35)(100)=80% k=(26.25/35)(100)=75% e=(22)(0.90)=20

∴Bala received 28 out of 35, Jonathan received 26.25 out of 35, and Disha got 90%.

36. Let j represent the numerator in the mark out of 35 for Jonathan, b represent the numerator in the mark out of 35 for Bala, and d represent the percentage Disha received. Given: j / 35 x 100 = 75 b / 35 x 100 = 80 20 / 22 x 100 = d On the test, Jonathan received: j / 35 x 100 = 75 35 ( j / 35 x 100 ) = 75 x 35 j x 100 / 100 = 2625 / 100 ∴ j = 26.25 Check: LS | RS j / 35 x 100 | 75 for j = 26.25: | 26.25 / 35 x 100 | 75 0.75 x 100 | 75 75 | 75 ∴ LS = RS √ ∴ Jonathan received a mark of 26.25 out of 35. On the test, Bala received: b / 35 x 100 = 80 35 ( b / 35 x 100 ) = 80 x 35 b x 100 / 100 = 2800 / 100 ∴ b = 28 Check: LS | RS b / 35 x 100 | 80 for b = 28: | 28 / 35 x 100 | 80 0.8 x 100 | 80 80 | 80 ∴ LS = RS √ ∴ Bala received a mark of 28 out of 35. On a different test, Disha received: 20 / 22 x 100 = 90% ∴ Disha received 90% on her test. [sjeyakanthakumar]

<span style="font-family: Verdana,Geneva,sans-serif;">

38. Let m represent the amount money group 4 had. Given: 2m + 2m - 20 + 3(2m) + m + 2m = £500

2m + 2m - 20 + 3(2m) + m + 2m = 500 2m + 2m + 6m + m + 2m = 500 + 20 13m = £520 m = £40

Check: 2m + 2m - 20 + 3(2m) + m + 2m 500 let m be 40 2(40) + 2(40) - 20 + 3[2(40)] +40 + 80 500 80 + 80 - 20 + 240 + 40 + 80 500 500 500 LS = RS

Therefore: group 1 gave 2m - 40 = £40 extra group 2 gave 2m - 20 - 40 = £20 extra group 3 gave 6m - 40 = £200 extra group 4 gave m - 40 = £0 extra group 5 gave 2m - 40 = £40 extra

<span style="font-family: Verdana,Geneva,sans-serif;"> 39. Let "a" represent Annie's amount of money she was to receive.

Jerry: 1000 + a David: (1000 + a) Annie: a

Jerry's share + David's share + Annie's share = 10 000 Given: (1000 + a) + (1000 + a - 700) + a = 10 000 1300 + 3a = 10 000 3a = 10 000 - 1300 3a/3 = 8700/3 ∴ a = 2900 __**Check**__ :


 * <span style="font-family: Verdana,Geneva,sans-serif;">__**Left Side**__

1000 + a + 1000 + a - 700 + a for a= 2900 1300 + 3a 1300 + 3(2900) 1300 + 8700 10 000 || <span style="font-family: Verdana,Geneva,sans-serif;">**__Right Side__**

10 000

10 000 || <span style="font-family: Verdana,Geneva,sans-serif;">∴ RS = LS

Result: Jerry's share: 1000 + a 1000 + 2900 3900

David's share: (1000 + a) - 700 (1000 + 2900) - 700 3900 - 700 3200

Annie's share: a = 2900

∴ Jerry was to receive $ 3900, David was to receive $ 3200, and Annie was to receive $ 2900.

<span style="font-family: Verdana,Geneva,sans-serif;"> 43. Given:If the volume of one block of clay is V=s³=10³=1000 cm³, then for two blocks of the same clay, the total volume would be 1000+1000=2000 cm³. The volume of the given sphere is V=4/3¶r3 =4/3¶(5)3= 125(4/3)¶=166.7¶=523

∴ You can make about 2000/523=4 spheres. [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 44. let w represent the width of the walkway the original dimensions are 20 m by 15 m the new dimensions for the outer perimeter of the walkway would be l= 20 + 2w & w= 15 + 2w P= 2(l+w) for P=78 2((20 + 2w) + (15 +2w)) = 78 40 + 4w + 30 + 4w = 78 70 + 8w = 78 8w/8 = 8/8 w = 1 ∴ The width of the walkway is 1 m. (sshanmuganantham)

<note to sshanmuganantham: Thanks for catching my mistake. > [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 45. Let n represent the number.

Given: n-18=-5n n+5n=18 6n=18 n=3 ∴ The number is 3. [kevink2435]

47. a) Let w represent the number of words she can type in 13 minutes.

Given: 300/5 as w/13 300/5=w/13 5w/5=3900/5 w=780 ∴ Judith can type 780 words. b) Let m represent the time in minutes. Given: 300/5 as 5756/m 300/5=5756/m 300m/300=28780/300 m=95.9=96 ∴ She would take 96 minutes. [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 48. Given: Out of the 1 km distance, Kevin ran 5 h ×<span style="font-family: Verdana,Geneva,sans-serif;">14 m/h=70 m in 5 hours. There is 1000 m in 1 km. For the rest of the way, Kevin's mom drove him 1000 m-70 m=930 m. If she drove at a speed of 100 m/h, then she would reach Kevin's school in 930/100=9.3 h.

∴ If Kevin left for school at 3:00 A.M., it would be 03:00 + 5 h+ 9h18= 17:18 or 5:18 P.M. by the time he reaches his school. He sure is LATE! [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 49. Let k represent Kevin's allowance. Let s represent Kevin's sister's allowance. Let c represent the constant of variation.

Given: k=cs² For k=0.9, s=0.5: 0.9=c(0.5)² -c=0.25-0.9 -c=-0.65 c= 0.65

k=cs² For s=22, c=0.65: k=0.65(22)² k=0.65(484) k=314.6

∴ Kevin's allowance would be k=$314.6. [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 52. Let n represent the original number of people at the party.

Given: There were originally n/2 boys and n/2 girls at the party.

2(n/2 - 5)= n/2 2(n-10)=2(n/2) 2n-20=n -20=n-2n -20=-n n=20 ∴ There were originally n=20 people at the party. [kevink2435]

53. Given: In total, there are 1+2+4+5=12 parts of cookies. ∴ Carolyn gets (1/12) × 24=2 cookies Melissa gets (2/12)× 24=4 cookies Areej gets (4/12)× 24=8 cookies Eleanor gets (5/12 ) × 24=10 cookies [kevink2435]

<span style="font-family: Verdana,Geneva,sans-serif;"> 55. Let q be the amount of quarters and 2q be the amount of dimes Given : 2 x quarters=dimes quarters value+dimes value=5.40 amount of quarters(0.25)+amount of dimes (0.10)=5.40 amount of quarters(0.25)+2 x amount of quarters (0.10)=5.40 q(0.25)+2q(0.10)=5.40 0.25q+0.2q=5.40 0.45q=5.40 q=5.40/0.45 q=12

check: given:0.25q+0.2q l 5.40 for q=12: 0.45(12) l 5.40 5.40 l 5.40 ∴ LS = RS √

∴ the amount of quarters is q=12 the amount of dimes is 2q=2(12) = 24 [m_sanghvi, l_leung, YYuan]

56. Given: = {-8-(-4)}/{4-2} = -4/2=-2

y=mx+b For m=-2, x=2, y=-4: -4=-2(2)+b -4=-4+b -4+4=b ∴ b=0 ∴ The line formula for this line is y=-2x [kevink2435]

57. Given:={3-0}/{3-3}= 3/0

∴ No, the line has an undefined slope because 3/0 not=0. [kevink2435]

58. Given:={3-3}/{2-0}=0/2

∴ Yes, the line has a slope of 0 because 0/2=0. [kevink2435]

59. The line would pass through 3 quadrants: 1,2, and 3. [kevink2435]

60. Given: Equation for Line 1: y=mx+3 For (-1,5) : 5=m(-1)+3 5-3=-m 2=-m m=-2

∴ m is -2

Equation for Line 2: y=-4x+b For (-1,5) : 5=-4(-1)+b 5=4+b b=1 ∴ b is 1

∴ m+b=-2+1=-1 [kevink2435]

61. ∴ The lines are parallel to each other because while the lines have the same slope, the points along the lines do not belong in the same family.

[kevink2435]

62. Let c represent the amount that Cleo would have spent at the Stitches warehouse. Ramaya then spent 5c and Jennifer then spent 1/3c Given: c+5c+1/3c=76 6c+1/3c=76 19/3c×3=76×3 19c=228 c=12 1/3c=4 ∴Jennifer would have spent 1/3c=$4 at the warehouse. [kevink2435]

63. Let h represent the number of hours that Edward takes to catch up with Ron. Given: 50h+12.5<65h 12.5<65h-50h 12.5/15<15h/15 h>0.8 ∴ Edward needs at least 0.8 h or 50 min. ∴ Edward will catch up with Ron at 11:50 A.M. [kevink2435]

64. Given: 2+3+5+x=4² 10+x=16 x=16-10 x=6 ∴The value of x is 6. [kevink2435]

65. We know that Dove hand soap costs $4.20 and is represented as 4 in the ratio; 6:4. let o represent the amount of one: - $4.20 ––—— = o - 4 $1.05 = o We now must multiply $1.05 by 6. $1.05 x 6 = $6.30

∴ the cost of Dial hand soap is $6.30.

66. given: Lisa;jack=20:14 votes there are 170 votes all together

20+14=34 parts all together 34/170 is 5 parts

lisa: 20x5=100 votes all together jack:14x5=70 votes all together

check: votes lisa got+votes jack got=170 100+70=170 LS=RS

∴ Jack got a total of 70 votes. [m-yang, aashraf1]


 * __Challenging Questions (Answers)__

Challenge Question # 3:**

<span style="font-family: Verdana,Geneva,sans-serif;">Let p represent how much Kevin was paid in 20 hours.

given: $132 in 9 hours

payment for 1 hour = $132 ÷ 9 total payment = $132 ÷ 9 × 20 = p p = 132 × 20 ÷ 9 <span style="color: rgb(255, 255, 255);">`~ = $293.33

check: 132 × 20 ÷ 9|293.33 <span style="color: rgb(255, 255, 255);">`~`~ 2640 ÷ 9|293.33 <span style="color: rgb(255, 255, 255);">~`~`~` 293.33|293.33 ∴LS = RS √ ∴ Kevin gets paid $293.33 in 20 hours.

[//hli//]

**Challenge Question #6**:

//Answer:// 3³

[//a_zhang//]