Sam is 2 years older than her brother. 12 years ago, she was twice as old as he was. How old are they now?
The best way to learn to set up word problems is to practice
looking up the answer first, then checking it to see why it is
the correct answer. That's because it takes te same thinking
to check a problem as it does to set it up.
So I'll start by telling you the answer. Then we'll set it up
to show how it was obtained, and you'll see it was the same
thinking as checking the problem:
The answer: Her brother is 14, so Sam is 16.
Checking:
Sam is 2 years older than her brother, who is 14, so she is 14+2, (or 16).
12 years ago, she was 16-12, (or 4) and he was 14-12, (or 2), and 4 equals
twice 2, so she was twice as old as he was.
Let B = her brother's age
Setting it up:
Sam is 2 years older than her brother, who is B, so she is B+2.
12 years ago, she was (B+2)-12 and he was B-12, and (B+2)-12 equals
twice B-12, so she was twice as old as he was.
To set up the equation you only need these words:
(B+2)-12 equals twice B-12
or
(B + 2) - 12 = 2(B - 12)
Solve that and get B = 14, then Sam is 2 years older, or 16.
Edwin
