Question

The variables $a$ and $b$ are inversely proportional. When the sum of $a$ and $b$ is 24, their difference is 6. What is $b$ when $a$ equals 5?

Answer 1

When a is equals to 5, b will be 27.

Step-by-step explanation:

Given variables are a and b;

The sum of a and b is 24.

a+b = 24    Eqn 1

Their difference is 6.

a-b = 6       Eqn 2

Adding equation 1 and 2

$(a+b)+(a-b)=24-6\\a+b+a-b=18\\2a=18$

Dividing both sides by 2

$\frac{2a}{2}=\frac{18}{2}\\a=9$

Putting a = 9 in Eqn 1

$9+b=24\\b=24-9\\b=15$

As a and b are inversely proportional;

$a$∝$\frac{1}{b}$

$a=\frac{k}{b}$

Where k is constant of proportionality.

k = ab

k = 15*9 = 135

Putting a=5

$5*b=135\\5b=135$

Dividing both sides by 5

$\frac{5b}{5}=\frac{135}{5}\\b=27$

When a is equals to 5, b will be 27.

Keywords: inverse proportion, multiplication

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