Math homework please, Word Problem?

Question

Can anyone show me how to solve this problem?

The difference between two numbers is 9. The sum of twice the larger number and three times the smaller number is 33. Find the two numbers.

Answer 1

Let the larger number be "a" and the smaller be "b".

You have two equations:

(1) a - b = 9 ("difference is nine")
(2) 2a + 3b = 33 ("twice the larger plus three times the smaller is 33")

Rearranging the first equation, we get a = b+9

Substituting b+9 for a into the second equation, we get:

2a + 3b = 33
2(b+9) + 3b = 33
2b + 18 + 3b = 33
5b = 15
b = 3

Since a = b+9, and b=3, we know a=12.

Now, to check, with the second equation:

2a + 3b = 33 ?
2(12) + 3(3) = 33 ?
24 + 9 = 33