Question

Michelle bought 50 meters of speaker wire for her new surround-sound speakers for $47.95. What is the constant of variation for this direct variation?

A) $0.959.
B) $0.959/meter.
C) $47.95.
D) 50.

Answer 1

The constant of variation for the direct variation of the cost of speaker wire to its length is found by dividing the cost by the length, giving a constant of $0.959/meter, making option B) the correct answer.

Step-by-step explanation:

The constant of variation in a direct variation is the ratio of the dependent variable to the independent variable. In this case, the dependent variable is the cost of the speaker wire, and the independent variable is the length of the wire. To find the constant of variation, we divide the total cost by the total length of wire.

The formula for the constant of variation, k, is:

k = total cost / total length

Using the values given:

k = $47.95 / 50 meters

Therefore, the constant of variation is:

k = $0.959/meter

The correct answer from the options given is B) $0.959/meter.