AnswersGA-8th Grade MathematicsModeling Real-World Multistep Equations

Modeling Real-World Multistep Equations Answers

16 verified answers3 views
1
Free Preview

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
Free Preview

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.
11

Aviva is comparing her age to her sisters’ ages. Kanti is 3 years younger. Aviva’s older sister, Lakshmi is twice as old as Kanti. Which expression correctly completes the table?Sister’s AgesSisterAgeAvivaxKantix – 3Lakshmi?

A
2 x minus 3
Option A
B
2 (x minus 3)
Option B
C
2x
D
(x minus 3) + 2
Option D
12

A rectangle has a width of x and a length that is 13 less than twice its width. Which rectangle shows the same relationship?

A
A rectangle with a length of 2 x minus 13 and width of x.
Option A
B
A rectangle with a length of 2 (x minus 13) and width of x.
Option B
C
A rectangle with a length of x + 2 and width of x minus 13.
Option C
D
A rectangle with a length of 13 minus 2 x and width of x.
Option D
13

Danessa is working with consecutive even numbers. If x is her first number, which expression represents her second number?

A
x + 1
B
x – 1
C
x + 2
D
2x
14

Roderick is counting the change on his dresser. He has twice as many pennies as he does dimes. He has twice the amount of dimes as he does nickels. He has 3 fewer quarters than dimes. Which variable definition would be easiest for Roderick to use when writing expressions for the number of all the coins?

A
x = number of pennies because the penny has the least value of all the coins.
B
x = number of nickels because there are fewer nickels than any other coin.
C
x = number of dimes because all the other coins are compared to dimes.
D
x = number of quarters because it has the greatest value of all the coins.
15

Jolianne worked half as many hours as Andrew. Jolianne makes $10 per hour and has saved $27. Andrew makes $8 per hour and has no money saved. After getting paid, they have the same amount of money. Andrew’s Table for Comparing MoneyNameRate of pay(per hour)Hours workedJolianne10Andrew8tAndrew’s equation: Jolianne’s Table for Comparing MoneyNameRate of pay(per hour)Hours workedJolianne10tAndrew82t Jolianne’s equation: Andrew claims that only his table and equation are correct, but Jolianne claims that both tables and equations are valid. Which statement regarding their claims is true?

Question illustration
A
Andrew is correct because t cannot be used to represent the number of hours Jolianne worked.
B
Andrew is correct because Jolianne worked half as many hours as he did and he did not work twice as many hours as she did.
C
Jolianne is correct because if one lets t = hours Andrew worked, then his equation is valid. If one lets t = hours Jolianne worked, then Andrew worked twice as many so her equation is valid, too.
D
Jolianne is correct because when solving t in her equation, t = hours Jolianne worked, and when solving for t in Andrew’s equation, t = hours Jolianne worked so they are equal.
16

Elliott is counting the change from a class fundraiser. He has half as many quarters as nickels, and he has 7 fewer dimes than nickels. The total value of coins is $5.90. He wrote the equation . Which statements identify Elliott’s errors? Select the two correct answers.

Question illustration
A
He should have written the expression for the number of dimes as x – 7.
B
He should have written the coin values as 5, 10, and 25 and not as 0.5, 0.10, and 0.25.
C
He should have written the coin value for the nickel as 0.05.
D
He should have translated the scenario as value of all dimes = value of all nickels and value of all quarters = value of all nickels.
E
He should have written the expression for number of nickels as 2x.

Did you find these answers helpful?

More from this Course

Quiz
6 verified answers

Modeling Real-World Multistep Equations

Quiz
16 verified answers

Equivalent Equations

Quiz
15 verified answers

Introduction to Functions