Question

50 points 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

12 years old

Explanation:

1) 2x+x=18

2) Now solve 2x+x=18

Add alike terms

3x=18

Now divide both sides by 3 (3x/3 and 18/3)

x=6

So Hannah is 6 years old. Her sister must be 12.

Answer 2

Explanation:

Let "Hannah" = h, and her sister = s

h = 2s

h + s ≤ 18

Plug in 2s for h in the second equation.

(2s) + s ≤ 18

Simplify

2s + s ≤ 18

3s ≤ 18

Isolate the variable (s). Divide 3 from both sides

(3s)/3 ≤ (18)/3

s ≤ 18/3

s ≤ 6

2) The oldest Hannah's sister can be is 6 years

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