Question

Sarah is researching the connection between the time students spend watching television and their performance in school. Her studies indicate that there is an inverse relationship between TV time and GPA, and that a student who watched 15 hours of TV per week can be expected to have a GPA of 3.5. Find k, the constant of variation, for this relationship.

A) 0.23
B) 4.29
C) 8.1
D) 52.5

Answer 1

Answer: D) 52.5

Explanation:

The equation for inverse variation between two quantities x and y is given by :-

`k=yx`, where k is the constant of variation, for this relationship. (1)

Given : Sarah studies indicate that there is an inverse relationship between TV time and GPA, and that a student who watched 15 hours of TV per week can be expected to have a GPA of 3.5.

Then from (1) the constant of variation is given by :-

`k=15*3.5=52.5`

Hence, the required answer is option D) 52.5 .

Answer 2

Her studies indicate that there is an inverse relationship between TV time and GPA, and that a student who watched 15 hours of TV per week can be expected to have a GPA of 3.5

In equation form

15 = k(1/3.5)

Solve for k

K = 15 * 3.5

K = 52.5 is the constant of variation