Question

The height of Moyo and that of

Adamu differs by 9. The difference of the squares of their height is 120.
Find their heights.​

Answer 1

The height of Moyo is

`(67)/(6)`

The height of Adamu is

`(13)/(6)`

Explanation:

Equations

To solve the problem, we assign the variable:

x = height of Moyo

Since Moyo is 9 units taller than Adamu:

x - 9 = height of Adamu

The difference of the squares of their heights is 120, thus:

`x^2-(x - 9)^2=120`

Operating:

`x^2-(x^2-18x+81)=120`

`x^2-x^2+18x-81=120`

Simplifying:

`18x-81=120`

Adding 81:

`18x=120+81=201`

Dividing by 18:

`x=(201)/(18)=(67)/(6)`

The height of Moyo is

`(67)/(6)`

The height of Adamu is

`(67)/(6)-9=(13)/(6)`