AnswersGA-8th Grade MathematicsModeling Real-World Multistep Equations

Modeling Real-World Multistep Equations Answers

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Three more than twice the sum of a number and half the number equals 105. Which equation models this relationship?

A
2 (x + one-half x) + 3 = 105
B
2 x + one-half x + 3 = 105
C
2 x + 3 = one-half x + 105
D
2 (x + 3) = one-half x + 105
2
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A rectangle has a length that is 8 less than its width, w. The perimeter is 52. Which equation can be used to determine its width?

A
8 minus w = 52
B
2 (w minus 8) + 2 w = 52
C
(w minus 8) + w = 52
D
2 (8 minus w) + 2 w = 52
3

Mrs. Craft bought pies for her math class to celebrate Day. The cream pies cost $1.50 more than the fruit pies. Mrs. Craft bought 3 cream pies and 4 fruit pies for $32.15.Cost of Cream PiesCreamCreamCreamp + 1.50p + 1.50p + 1.50Cost of Fruit PiesFruit FruitFruitFruitppppWhich equation represents this scenario?

Question illustration
A
p + (p + 1.50) = 32.15
B
3 p + 1.50 + 4 p = 32.15
C
3 (p + 1.50) + 4 p = 32.15
D
3 (p + 1.50) = 4 p
4

Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?

A
perimeter of the triangle
B
area of the triangle
C
side length of the triangle
D
height of the triangle
5

Braelyn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. She knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. Which equations represent this relationship? Select the four correct answers.

A
x + one-half x = 18
B
2 x + x = 18
C
2 (x) + 2 (2 x) = 18
D
x + one-half x + x + one-half x = 18
E
2 (x + one-half x) = 18
F
2 x + one-half x = 18
6

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers?

A
x + x + x = negative 21
B
x + 2 x + 3 x = negative 21
C
x + (x + 1) + (x + 2) = negative 21
D
x + (x + 2) + (x + 4) = negative 21
7

Three consecutive integers have a sum of 30. Which equation can be used to find x, the value of the smallest of the three numbers?

A
(x + 1) + (x + 2) = 30
B
x + (x + 1) + (x + 2) = 30
C
x (x + 1) (x + 2) = 30
D
3 x (x + 1) (x + 2) = 30
8

Garrett is creating a table to model the speed of a canoe in a river. He knows that the canoe travels at 4 mph in still water. What does x represent in Garrett’s table?Canoe SpeedDirection on riverSpeedWith current (downstream)4 + xAgainst current(upstream)4 – x

A
speed of current in river
B
speed of canoe upstream
C
time of trip
D
distance traveled
9

Kami and her mother offer tours of a nearby canyon. They charge a $50 base rate plus $10 per person for a 2.5 hour tour. Which equation represents A, the amount they make to tour p people thorough the canyon?

A
2.5 p + 50 = 10 A
B
10 p + 50 = A
C
2.5 p + 50 = A
D
StartFraction 10 Over p EndFraction + 50 = A
10

Bethany wrote the equation when she was told that the sum of three consecutive odd integers had a sum of 91. Which statement about her equation is true?

Question illustration
A
Bethany is correct because consecutive odd integers will each have a difference of two.
B
Bethany is correct because there are three xs in the equation and three is an odd number so it represents the sum of odd numbers.
C
Bethany is incorrect because 2 and 4 are even numbers, she should use 1 and 3 in their place.
D
Bethany is incorrect because consecutive integers always increase by 1 each time, not by 2.

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