The ages of three children add up to 27 Ben is twice as old as Adam, Caroline is 7 years older than Adam. Find the ages of all three children? Word problems.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Start by assigning variables. It is best, if possible, to then write each of the variables in terms of 1 variable (preferably the one you seek).

Let A be Adam's age, B be Ben's age, and C be Caroline's age.

Since A is Adam's age, A=A.

Since Ben is twice as old as Adam, B=2A. (Twice indicates multiplication by 2)

Since Caroline is 7 years older than Adam then C=A+7.

The sum of the ages is 27 so:

A+(2A)+(A+7)=27. Now collect like terms:

4A+7=27               Subtract 7 from both sides

4A=20                   Dicide both sides by 4 (Multiply both sides by 1/4 if you prefer)


Thus Adam is 5; this makes Ben 2(5)=10 and Caroline 5+7=12.

The three ages are Adam is 5 yrs, Ben is 10 yrs, and Caroline is 12 yrs.

** Checking we see that 5+10+12=27 and 10=2(5) and 12=5+7 as required. **

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team