Question

One half of a number increased by 16 is four less than two thirds of the number. What are the numbers?

Answer 1

The number is `color(green)(72)`

Explanation:

Let the number be `n`

the number increased by `16`
`color(white)("XXX")n+16`

one half of the number increased by `16`
`color(white)("XXX")1/2(n+16)`

two thirds of the number
`color(white)("XXX")2/3n`

one half of the number increased by `16`
is `4` less than
two thirds of the number
`color(white)("XXX")1/2(n+16)=2/3n-4`

Multiply both sides by `6` to get rid of the fractions
`color(white)("XXX")3(n+16)=4n-24`

Simplify
`color(white)("XXX")3n+48=4n-24`

Subtract `3n` from both sides
`color(white)("XXX")48=n-24`

Add `24` to both sides
`color(white)("XXX")72=n`
or
`color(white)("XXX")n=72`