Equations+Review+2

Model Answers The following model answers (and the questions, of course!) were created by the students of MPM1D1–EE.

p - 3 ÷ 7 + 3 ÷ 7 = 4 ÷ 7 + 3 ÷ 7 p = 7 ÷ 7 p = 1 6+//x =// 10 Therefore, there were 4 oranges in the basket. //x +// 12 = 30 //x=18 girls// Therefore, the class had 18 girls. 6) 7) 8) 9) 10) j + 7 = 18** j = 18 - 7 j = 11 Therefore, Josh has 11 dollars in his pocket. a = 8 + 9 a = 17 Therefore, Andie is 17 years old. 9 - 8.2 = x 0.8=x check: (do the equation again, but substitute x for your answer) LS= 9 RS= 8.2 = 0.8 LS= 9 RS= 9 LS=RS *check mark* y= 1/7+ 1/5 y= 6/7 check: (do the equation again, but substitute x for your answer) LS= 6/7 - 1/7 RS= 5/7 LS=RS *check mark* X= 220-5 X=215 Therefore john has 215 cards in total
 * 7.1**
 * 1)p – 3 ÷ 7 = 4 ÷ 7**
 * 2)** If you add – 3 + 2 to both sides of the equation the equation would decrease by one because – 3 + 2 = – 1.
 * 3) //let x be the number of oranges://**
 * //x =// 4 oranges **
 * 4)** **//let x represent the number of girls://**
 * 5)
 * 11) a - 9 = 8**
 * 12) 9=8.2+x**
 * 13) Y- 1/7 = 5/7**
 * 18)** X+5=220

1) 2) let //x// represent the number of pies needed:** 1/5//x =// 60 //x= 12 pies// Therefore, 12 pies are needed to feed 60 people. 1/3//x =// $2400 //x=// $800 Therefore, $800 will be donated and $1600, ($2400-$800), will be given to the school. 5) 6) 7) 8) 9) 2x = 98** x = 98/2 x = 49 Therefore, Kevin for 49% in the math test. a = 15 * 5 a = 75 Therefore, the side length of cube B is 75 cm. X=38.8 + 1.8 X= 40.6
 * 7.2
 * 3) let x represent the money that'll be given to the campaign:**
 * 4)
 * 10) a/5 = 15**
 * 11)** X-1.8=38.8

1)** **//let c represent Cherry's age://** 3m+5+m+m= 50 5m+5=50 5m=45 m= 9 years old Therefore, Cherry is 9 years old. 3y-6=24 3y=30 y=10 4) 5) 2y + 2 = 16** 2y = 16 - 2 2y = 14 y = 7 Therefore, Nicole is 7 years old. 10x = 200 x = 20 Therefore, 2x = 2 * 20 = 40 3x = 3 * 20 = 60 5x = 5 * 20 = 100 a=160x1.6 a=256 therefore beaker A has 256 cm3
 * 7.3
 * 2)** June divided first. She should've added 6 to both sides and then divide. The answer should be:
 * 3)
 * 6) 2x + 3x + 5x = 200**
 * 7)** a(divided) 1.6= 160

1) //let p be Paul's age now: Age of Julie now: x+30//** 3//x=// 1/2(//x+//30) +20 3//x//= 1/2//x//+15+20 3//x//-1/2//x=// 15+20 2 1/2//x =// 35 //x=// 14 years old Therefore: Julie: x+30 14+30 44 years old Paul: //x+//2 14+2 16 years old
 * 7.4

solve n' check

LS= 3(14) 1/2 =20 RS= 14 LS=RS `/ [V.Khan]

12//x//+8 = 8//x//-20 12//x-//8//x =// -20+8 4//x// = -12 //x= -3// 5) x + 12 = 5p** 12 = 5p - p 12 = 4p 3 = p Therefore, Lori has 3 pens. x - 4x = -6 -3x = -6 x = 2
 * 2)** (3//x+//2) /2 = (4//x//-10) /2
 * 4)
 * 6) p = 4x - 6**

1)** 2(//x+// $30) = //x-$20// 2//x+//$60 = //x- $20// 2//x-x// = -20+60 //x=//$40 Therefore: George: 2(//x+30)// 2($40+$30) 2($70) $140 in his acc. Jenny: //x-//$20 $40-$20 $20 in her acc.
 * 7.5

10+2//x// = 15+3//x-//12 10-15+12 = 3//x//-2//x// 7 = //x// Therefore: Goo: 3(5//+x-//4) 3(5+7-4) 3(8) 24 pencils Bob: 2(5+//x)// 2(5+7) 2(12) 24 pencils 4) 5) 2 (2n+3) + 2 (n+5) + 40** 4n + 6 + 2n -10 = 40 4n + 2n = 40 - 6+ 10 6n = 44 n = 7.3 Therefore, 2n + 3 = 2 * 7.3 + 3 = 17.6 n + 5 = 7.3 + 5 = 12.3 2x - 4 = 80 2x = 84 x = 42 Therefore, Ali's mark is 42%
 * 2)** 2(5+//x//) = 3(5+//x//-4)
 * 3)
 * 6) 2 (x-2) = 80**

2) 3)** //x+x+//1 = 45/2 2//x//+1 = 22.5 2//x// = 21.5 //x// =10.75 First number: 10.75, Second #: 10.75+1 = 11.75 1/2+//x// = 3 //x =// 3- 1/2 //x =// 2 1/2 slices Therefore, Kate has 3 slices and Lenny has 2 and 1/2 slices of pizza. 8x = 0.45 + 0.21 8x = 0.66 x = 0.08 Therefore, Abbey spends 0.08 of time without studying. b/5 = 10.5 - 2 b/5 = 8.5 b = 42.5 Therefore, Bess has 42.5 dollars.
 * 7.6**
 * 1)
 * 4) 1/2**+//x =// 1/3 (9)
 * 5) 8x - 0.21 = 0.45**
 * 6) b/5 + 2 = 10.5**

1) 2) 3)** 2(2//x+2)+2x//+2+10 = 30cm 9) 2w+t=56 2(t+10)+t=56 3t+20=56 3t=36, and so 'ties' equal to 12. w= t+10, and so 'wins' equal to 22.
 * 7.7
 * 4)** //x-//20 = 1/5 (100)
 * 5)** 4x + 6 = 42cm
 * 6)** 5x + 5 = 38cm

2) 3)** //x//+2+//x//+1+//x// = 15 3//x//+3=15 3//x//=12 //x =// 4 (6+L)(L) = 42 cm^2 6+L^2 = 42 cm^2 L^2= square root of 36 L=6cm Therefore, the length of the rectangle is 6cm and the width is 12cm, (6+6). 2x = 44 - 10 2x = 34 x = 17 Therefore Becky is 27 and Ron is 17 years old. x + x + x + x = 124 - 1 - 2 - 3 4x = 118 Therefore, x = 29.5 x + 1 = 29.5 + 1 = 30.5 x + 2 = 29.5 + 2 = 31.5 x + 3 = 29.5 + 3 = 32.5
 * 7.8**
 * 1)
 * 4) w=6+L, A=LxW**
 * 5) x +x +10 = 44**
 * 6) x + x + 1 + x + 2 + x + 3 = 124**

1) 2) 3)** //let x be the distance in km between Toronto and Paris. x///500 +//x///700 = 15 5600(//x///800+//x///700) = 15(5600) 7//x//+8//x// = 84000 15//x =// 84000 //x =// 5600km Therefore, the distance between Toronto and Paris is 5600 km. 5) p = 2(l+w)** 40 = 2(13+w) 40 = 26 + 2w 14 = 2w 7 = w Therefore, w, the width is 7cm. 56 = 4s 14 = s Therefore s, the side length of the square is 14 com. Which mean the width is 14 and the length is 14 too.
 * 7.9
 * 4)
 * 6) p = 4 (s)**

1)** 2.7
 * 7.1
 * 2)** 14 [HTahir]

1)** 5
 * 7.2
 * 2)** 5 [HTahir]

1)** 16
 * 7.3
 * 2)** 6 [HTahir]

1)** 10
 * 7.4
 * 2)** 0.6 [HTahir]

1)** -1
 * 7.5
 * 2)** 5 [HTahir]

1)** 2
 * 7.6
 * 2)** 4 [HTahir]

1) 7-x 2) 8x [HTahir]
 * 7.7**

1)** 34, 35, 36
 * 7.8
 * 2)** 20m by 25m [HTahir]

1)** 40cm
 * 7.9
 * 2)** 17m [HTahir]

1) 19,25,31 pattern is going up by 6 2) 16,20,24 pattern is going up by 4 [HTahir]
 * 7.10**

Hamza Khan Model Answers 7.1-7.5 #1-25 1.-11 = t -1, 1 -11= T, T= -10 2. X + 3= 9, 9 – 3= X, X=6 3. 2 + X = -4, -2 -4 = X, X = -6 4. 7 = X -5, 7 + 5 = X, X= 12
 * 7.1 **

5. X -1 = 5, 5 + 1 = 6, X= 6 1. 2Y = -12, -12/2Y = Y, Y = -6 2. 2X = -8, -8/2X = X, X = -4 3. 2X = 8.4, 8.4/2X = X, X = 4.2 4. X/3 = 9, 3 x 9 = X, X = 27 5. Y/7 = 4, 7 x 4 = Y, Y = 28 7.3 ** 1. 2- 1.8r = 11, 11-2 = 1.8R, 9/1.8R = R, R = 5 2. 2Y – 5 = 9, 9 + 5 =2Y, 14/2Y = Y, Y = 7 3. 3 + M = -7, -7 -3 = M, M = -10 4. 4 + X = 20, 20 -4 = X, X = 16 5. 5N + 2N = -14, 7N = -14, -14/7N = N, N = -2
 * 7.2 **

7.4 1. 7Y = 20 + 3Y, 7Y – 3Y = 20, 4Y = 20, 20/4Y =Y, Y =5 2. 3M = M + 4, 3M- M = 4, 2M = 4, 4/2M = M, M=2 3. 7N = 4N – 6, 7N - 4N = -6, 3N = -6, -6/3N=N, N=-2 4. 2X = -30 + 5X, 2X – 5X = -30, -3X = -30, -30/-3X= X, X= 15 5. 4N = 3.6 – 2N, 4N + 2N = 3.6, 6N = 3.6, 3.6/6N = N, N= 0.6

7.5 1. 2 (X – 3) = 2, 2X – 6 = 2, 2X = 8, 8/2X =X, X = 4 2. 2 (X + 6) = -6, 2X + 6 = -6, -12/2X = X, X = -6 3. 3 (2X + 3) = -3, 6X + 6 = -3, -9/6X = X, X = -1.5 4. 2 (X + 5) = -4, 2X + 10 = -4, -14/2X = X, X = -7 5. 2 (X + 1) = 4, 2X + 2 = 4, 2/2X = X, X = 1