Question

Hello, I need help in a compound inequality word problem:

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?

1. 0 2.0 3.0 4.0

Answer 1

3+2x<30

Explanation:

3 represents that Emily is 3 years older than 2x

2x represents twice Mary's age

<30 represents that it's always less than 30

Answer 2

The compound inequality is
`0<x<9`

Explanation:

Consider the provided information.

It is given that Emily is three years older than twice her sister Mary's age.

Let x represent Mary's age.

Then the age of Emily is: 2x+3

The sum of their ages is less than 30.

This can be written as:

`2x+3+x<30`

`3x+3<30`

`3x<27`

`x<9`

As we know the age can't be a negative number.

Therefore, the age of Mary must be a positive number greater than 0.

Thus, the compound inequality is
`0<x<9`