Question

Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.

1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.

Answer 1

1)
`2s+s\leq18`

2) 6 years old

Explanation:

Let Hannah's age be
`h` and her sister's age be
`s`

• Hannah is 2 times her sister’s age:

It means
`h=2s`

• The sum of their ages is no more than 18 years:

It means the sum is LESS THAN or EQUAL TO 18. So we can write:

`h+s\leq18`

1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,

`h+s\leq18\\2s+s\leq18`

2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,

`2s+s\leq18\\3s\leq18\\s\leq(18)/(3)\\s\leq6`

Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.