INVESERSE VARIATION

QUESTION : if a varies inversely as b and a = 1/4 when b = 6, find a when b = 24.

GIVEN : a = 1/4, b = 6

EQUATION : a = k/b

SOLUTION : The statement, "a varies inversely as b" translated into directly variation is a = k/b where k is the constant of variation.

Solve if a is 1/4 and b is 6. So, find the constant using the equation of inverse variation.

• a = k/b
• 1/4 = k/6
• 0.25 = k/6
• 0.25 × 6 = k
• 1.5 = k or k = 1.5

The constant of the variation is 1.5 in equation of variation.

• a = 1.5/b

Find a when b is 24. Substitute the equation using the constant of the variation.

• a = 1.5/b
• a = 1.5/24
• a = 0.0625

ANSWER : The value of a is 0.0625

QUESTION

If a varies inversely as b and a = 1/4 when b=6, find a when b=24.

SOLUTION

a = k/b

1/4 = 6/k

0.25 = 6/k

0.25 • 6 = k

k = 1.5

Find a when b is 24.

a = 1.5/b

a = 1.5/24

a = 0.0625