Question

Suppose c and d vary inversely, and d=2 when c=17.

a. Write an equation that models the variation.
b. Find d when c=68.

Answer 1

a. x - cd = 0

b. d = 1 / 2

Explanation:

d = 2

c = 7

a.

c is inversely proportional to d,

c ∝ 1 / d

This inversely proportional need to be removed by using a variation / variable.

Let the variable be " x ".

c = x / d

Multiply d on both sides,

cd = x

x = cd

Subtract cd on both sides,

x - cd = 0

Hence, the equation is " x - cd = 0 ".

b.

By using the equation,

x - cd = 0

Add cd on both sides,

x = cd

c = 17, d = 2

x = 17 * 2

x = 34

To find d, when c = 68.

x = cd

34 = 68 * d

Divide 68 on both sides,

34 / 68 = d

1 / 2 = d

d = 1 / 2