Question 1181825: Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old is Carmen now? Found 4 solutions by Darshil, greenestamps, josgarithmetic, MathTherapy:Answer by Darshil(1) (Show Source): You can put this solution on YOUR website! Let assume that Carmen's age is x, & David's age is y.
Carmen is 12 years older than David Hence,
x = y + 12 ---- (1)
Especially when you are first learning algebra, look for different ways of setting problems up. There are dozens of ways to set up this problem for solving using formal algebra; different ways of setting the problem up can make big differences in the amount of work required to find the answer.
The solution from the other tutor is fine -- but it translates the given information directly into equations, which leads to a solution requiring much more work than necessary.
Here is how I would set this problem up.
Do some simple mental work with the given information to make it easier to use:
"Five years ago, the sum of their ages was 28."
So now the sum of their ages is 28+10=38.
Since Carmen is 12 years older than David, let their ages be x+12 and x. Then
Let Carmen's age be C
Then David's is: C - 12
Since their ages summed to 28, 5 years ago, we get: C + C - 12 - 2(5) = 28
2C - 12 - 10 = 28
2C - 22 = 28
2C = 50
Carmen's age, or