Question

Lenny is eight years older than twice her cousin Sue's age. The sum of their ages is less than 32. What is the greatest age that Sue could be?

Answer 1

Sue can be, at greatest, 7 years of age.

Explanation:

Lenny's age is `L`.
Lenny is eight years older(8+) than twice her cousin Sue's age (2S, as `S` is Sue's age)

Therefore,
`\color(red)(L=8+2S)`

The sum of their (Lenny and Sue) ages is less than 32.
`L+S\lt32`

Do you notice that there is already an equation for `L` that contains `S` (in red)? Let's substitute that into the inequality we just mentioned.

`(\color(red)(8+2S))+S\lt32`
Simplifying...
`8+3S\lt32`
`3S\lt32-8`
`3S\lt24`
`S\lt24/3`
`S\lt8`

Since Sue cannot be 8, the oldest (greatest age) she can be is 7 years old.