Question

A varies jointly as of the product of b and c. If a = 24 when b = 8 and c = 2, find b when a = 48 and c = 4.

Answer 1

Variation can be direct, inverse or joint.

The value of B when a = 48 and c = 4 is 8

The joint variation is represented as:

$A \ \alpha\ BC$

Express the variation as equation

$A = kBC$

Make k the subject of the formula

$k= \frac{A}{BC}$

If a = 24 when b = 8 and c = 2, we have:

$k = \frac{24}{8 \times 2}$

$k = \frac{24}{16}$

$k = 1.5$

So, $A = kBC$ becomes

$A = 1.5BC$

Make B the subject

$B = \frac{A}{1.5C}$

When a = 48 and c = 4, we have:

$B = \frac{48}{1.5 \times 4}$

$B = \frac{48}{6}$

Divide

$B = 8$

Hence, the value of B is 8

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