Question

Emily is three years older than twice her sister Mary's age. The sum of their ages is less than 30. Let x represent Mary's age. Which inequality represents Mary's possible age?

Answer 1

0 < x < 9

Explanation:

Mary's age = x

Twice of Mary's age = 2x

Emily's age = (2x + 3) (we are told Emily is 3 years older than twice of Mary's age)

Given that the sum of their ages is > 30, we have the following expression:

`(2x + 3) + x` > 30

Let's simply:

`2x + 3 + x` > 30

`3x + 3` > 30

Subtract 3 from both sides

`3x + 3 - 3` >
`30 - 3`

`3x` >
`27`

Divide both sides by 3

`(3x)/(3)` >
`(27)/(3)`

`x` >
`9`

Therefore, the inequality that represents Mary's possible age is: 0 < x < 9