# Test Your Knowledge On Direct Variation

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| By Ahollifield
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Ahollifield
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Quizzes Created: 7 | Total Attempts: 4,780
Questions: 11 | Attempts: 577

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• 1.

### Which of the following is the correct equation for the following if y varies directly as x? x =3 and y = 4.

• A.

Y = (3/4)x

• B.

Y = (4/3)x

• C.

Y = 1x

• D.

Y = -1x

B. Y = (4/3)x
Explanation
If y varies directly as x, it means that y is directly proportional to x. This means that as x increases or decreases, y will also increase or decrease by the same factor. In this case, when x = 3, y = 4. To find the equation, we can set up a proportion: y/x = k, where k is the constant of variation. Plugging in the values, we get 4/3 = k. Therefore, the correct equation is y = (4/3)x.

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• 2.

### Assume y varies directly as x.  If y = 20 and x  = 4, find y when x = 9.

• A.

Y = 9/5

• B.

Y = 180

• C.

Y = 14

• D.

Y = 45

D. Y = 45
Explanation
In this problem, we are given that y varies directly as x. This means that as x increases, y also increases proportionally. We are given that when x = 4, y = 20. To find y when x = 9, we can use the concept of direct variation. We can set up a proportion using the given values: 4/20 = 9/y. Cross-multiplying gives us 4y = 180. Dividing both sides by 4, we find that y = 45. Therefore, the correct answer is y = 45.

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• 3.

### If y = 15 when x = 2, then y = 10 when x = 8.  True or False?

• A.

True

• B.

False

B. False
Explanation
The given statement is false because there is no direct relationship or equation provided between y and x. Therefore, we cannot determine the value of y when x is 8 based on the given information.

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• 4.

### Y is directly proportional to x. If y = 16 when x = 4, write the formula to represent this relation of y and x.

• A.

Y = 4x

• B.

Y = (1/4)x

• C.

Y = 12x

• D.

Y = 20x

A. Y = 4x
Explanation
The formula y = 4x represents the given relation of y and x because it states that y is directly proportional to x with a constant of 4. This means that as x increases or decreases, y will also increase or decrease by a factor of 4 times the value of x.

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• 5.

### The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. The amount of money raised for 5 attendees was \$100. How much money will be raised for 60 attendees?

• A.

\$80

• B.

\$6,000

• C.

\$1,200

• D.

\$12,000

C. \$1,200
Explanation
The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. This means that as the number of attendees increases, the amount of money raised will also increase. In this case, we are given that for 5 attendees, \$100 was raised. To find out how much money will be raised for 60 attendees, we can set up a proportion. If \$100 is raised for 5 attendees, then we can set up the proportion 100/5 = x/60, where x represents the amount of money raised for 60 attendees. Solving this proportion, we find that x = \$1,200. Therefore, \$1,200 will be raised for 60 attendees.

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• 6.

### Which of the following is NOT true about direct variation?

• A.

Direct Variation is y = k/x

• B.

Direct variation is y = kx

• C.

Direct variation always passes through the origin (0,0)

• D.

Direct variation has a constant of proportionality, k.

A. Direct Variation is y = k/x
Explanation
Direct variation is a mathematical relationship between two variables, where one variable is a constant multiple of the other. The equation y = k/x does not represent direct variation because it involves division, whereas direct variation is represented by the equation y = kx, where k is the constant of proportionality. Additionally, direct variation does not always pass through the origin; it can pass through any point on the coordinate plane. Therefore, the statement "Direct Variation is y = k/x" is not true about direct variation.

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• 7.

### The cost of mailing a box varies directly with the weight of the box in pounds.  It costs \$8 to mail a 5-pound box.  How much would it cost to mail a 12-pound box?

• A.

\$19.20

• B.

\$16.00

• C.

\$15.00

• D.

\$7.50

A. \$19.20
Explanation
The cost of mailing a box varies directly with the weight of the box. This means that as the weight of the box increases, the cost of mailing it also increases proportionally. In this case, the cost of mailing a 5-pound box is \$8. To find the cost of mailing a 12-pound box, we can set up a proportion: 5 pounds is to \$8 as 12 pounds is to x dollars. Solving this proportion, we find that x = \$19.20. Therefore, it would cost \$19.20 to mail a 12-pound box.

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• 8.

### The Outboard Motor Company can produce 50 motors in 4 weeks.  Assuming a direct variation, how many motors can the company produce in 10 weeks?

• A.

75 motors

• B.

125 motors

• C.

150 motors

• D.

200 motors

B. 125 motors
Explanation
The given problem states that The Outboard Motor Company can produce 50 motors in 4 weeks. This implies that the production rate is directly proportional to the number of weeks. To find out how many motors can be produced in 10 weeks, we can set up a proportion: 50 motors/4 weeks = x motors/10 weeks. Solving this proportion, we can cross multiply and get 4x = 500, which simplifies to x = 125. Therefore, the company can produce 125 motors in 10 weeks.

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• 9.

### The distance it takes to stop a moving train varies directly with the speed it is traveling.  A train that is moving 50 mph required 10,000 feet to stop. How many feet will be required to stop a train moving 45 mph?

• A.

225 feet

• B.

1111.11 feet

• C.

900 feet

• D.

9000 feet

D. 9000 feet
Explanation
The question states that the distance required to stop a moving train varies directly with its speed. This means that as the speed of the train decreases, the distance required to stop it will also decrease. Since the train moving at 50 mph required 10,000 feet to stop, it can be inferred that a train moving at a lower speed of 45 mph will require a shorter distance to stop. Therefore, the correct answer is 9000 feet.

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• 10.

### Katherine sells 75% of the cupcakes that she sells at her bakery.  Which term would correctly describe which part of the direct variation equation 75% would represent?

• A.

Y variable

• B.

X variable

• C.

Constant of proportionality

• D.

Product

C. Constant of proportionality
Explanation
The correct term to describe the part of the direct variation equation that represents 75% is the constant of proportionality. In a direct variation equation, the constant of proportionality represents the ratio between the two variables. In this case, it represents the ratio between the number of cupcakes sold and the total number of cupcakes sold. Since Katherine sells 75% of the cupcakes, the constant of proportionality would be 0.75, indicating that for every cupcake sold, 0.75 cupcakes are sold.

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• 11.

### Since Katherine sells 75% of her cupcakes, how many cupcakes could she expect to sell on a day with 200 customers assuming that they all purchase two cupcakes each?

• A.

300 cupcakes

• B.

15,000 cupcakes

• C.

150 cupcakes

• D.

250 cupcakes

A. 300 cupcakes
Explanation
If Katherine sells 75% of her cupcakes, it means that she sells 3/4 of the total number of cupcakes. Assuming each customer purchases two cupcakes, she would sell 2 cupcakes to each customer. Therefore, to find the total number of cupcakes she would sell, we multiply the number of customers (200) by the number of cupcakes each customer purchases (2), which equals 400. Since she sells 3/4 of the total cupcakes, we multiply 400 by 3/4, which gives us 300 cupcakes.

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• Current Version
• Mar 22, 2023
Quiz Edited by
ProProfs Editorial Team
• Nov 28, 2011
Quiz Created by
Ahollifield

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