Question

Select the correct answer.

Lance is knitting a blanket and needs to buy some more yarn. At his local craft store, 2 balls of yarn cost $5 and 8 balls of yarn cost $20. What is the constant of proportionality in this direct variation situation?

A. 5/2
B. 2/5
C. 5
D. 2

Answer 1

The constant of proportionality in the given direct variation situation, where the cost of yarn is directly proportional to the number of balls of yarn purchased, is 2/5. This represents the cost per ball of yarn, with each ball costing $2.5.

Step-by-step explanation:

The question asks for the constant of proportionality in a direct variation situation where 2 balls of yarn cost $5 and 8 balls of yarn cost $20. To find the constant of proportionality, you divide the total cost by the number of balls of yarn. In this case, $5/2 balls gives us $2.5 per ball, and $20/8 balls also gives us $2.5 per ball. This confirms that the constant of proportionality is the same in both cases, demonstrating a direct variation.

The correct answer is thus B. 2/5, since the cost per ball of yarn is $2.5, which can be represented as 2.5/1 or 5/2 for the ratio of cost to the number of balls. Therefore, the constant of proportionality, when expressed as the cost per single ball of yarn, is 2/5.

Answer 2

The constant of proportionality in this direct variation situation is $2.50.

Step-by-step explanation:

In a direct variation situation, the constant of proportionality is the ratio of the two quantities.

In this case, the constant of proportionality can be found by dividing the cost of 2 balls of yarn ($5) by the number of balls (2):

Constant of proportionality = Cost of 2 balls / Number of balls = $5 / 2 = $2.50.

Therefore, the correct answer is A. 5/2.