AnswersHCISD-Mathematical Models with Applications B-CR SUMMEREquations of Proportional Relationships

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1
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Why are the solutions to the proportions and the same?

Question illustration
A
because both result in the equation , which simplifies to
Option A
B
because both result in the equation , which simplifies to
Option B
C
because both result in the equation , which simplifies to
Option C
D
because both result in the equation , which simplifies to
Option D
2
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A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?

A
StartFraction 3 over 63 EndFraction = StartFraction m over 7 EndFraction
Option A
B
StartFraction 7 over 63 EndFraction = StartFraction m over 3 EndFraction
Option B
C
StartFraction 63 over 3 EndFraction = StartFraction m over 7 EndFraction
Option C
D
StartFraction 63 over 7 EndFraction = StartFraction m over 3 EndFraction
Option D
3

Why are the solutions to the proportions and the same?

Question illustration
A
because both result in the equation , which simplifies to
Option A
B
because both result in the equation , which simplifies to
Option B
C
because both result in the equation , which simplifies to
Option C
D
because both result in the equation , which simplifies to
Option D
4

Why is x = 4 a solution to the proportion ?

Question illustration
A
because 56 divided by 14 is equal to 4
B
because 56 divided by 16 is equal to 4
C
because if you substitute 4 into the equation for x and cross multiply, you get
Option C
D
because if you substitute 4 into the equation for x and cross multiply, you get
Option D
5

Why can you use cross products to solve the proportion for x?

Question illustration
A
because 18 times 100 is equal to 5 times x, which means that x is equal to 36
B
because 18 times 100 is equal to 5 times x, which means that x is equal to 360
C
because 18 times x is equal to 5 times 100, which means that x is equal to 36
D
because 18 times x is equal to 5 times 100, which means that x is equal to 360
6

What is the value of x in the proportion ?

Question illustration
A
2 and two-fifths
Option A
B
5 and two-fifths
Option B
C
8 and StartFraction 1 over 10 EndFraction
Option C
D
12 and StartFraction 3 over 20 EndFraction
Option D
7

Which equation could you use to solve for x in the proportion ?

Question illustration
A
4 x = 14
Option A
B
4 x = 45
Option B
C
5 x = 13
Option C
D
5 x = 36
Option D
8

What is the solution to the proportion? Round the answer to the nearest tenth if necessary.

Question illustration
A
x = 14.6
Option A
B
x = 17.8
Option B
C
x = 157.8
Option C
D
x = 169.0
Option D
9

Isabella worked 50 hours over the past two weeks, and she gets paid by the hour. During the first week of the two-week span, she worked 30 hours and got paid $285.00. How much did she get paid during the second week of the two-week span?

A
$114.00
B
$190.00
C
$427.50
D
$475.50
10

Joanie believes that you cannot use cross products to solve the proportion for x. She says that if you multiply both sides of the equation by x, you get . Then, if you multiply both sides of the equation by 3, you get , which is a different equation than you would get if you cross multiplied. What mistake did Joanie make in her reasoning?

Question illustration
A
She assumed that the multiplication property of equality allows her to multiply both sides of the equation by x.
Option A
B
She assumed that the multiplication property of equality allows her to multiply both sides of the equation by 3.
Option B
C
She assumed that is the equation that you get if you multiply both sides of the equation by 3.
Option C
D
She assumed that is the equation that you get if you multiply both sides of the equation by x.
Option D

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