The larger of two numbers is four more than three times the smaller number. If the sum of the number is 120, find the numbers.

Answer 1

Any time you have a word problem, start by trying to turn the words into mathematical symbols. Let's call the Larger number L and the smaller number S.

The larger of 2 numbers is 4 more than three times the smaller -- L - 4 = 3S

The sum of the number is 120 -- L + S = 120.

You cannot solve an equation with two different variables (L and S), so we need to find a way to get rid of one of them. Using the second equation L + S = 120, we can subtract S from both sides to get L = 120 - S.

Now go back to the first equation -- L - 4 = 3S. Instead of using L, we'll use 120 - S. So now we have 120 - S - 4 = 3S.

120 - 4 = 116. 116 - S = 3S

Add S to both sides to get the regular numbers on one side and the Ss on the other. 116 = 4S

Divide both sides by 4 to get S completely by itself. 29 = S

Now that we know the smaller number is 29, we can use L + S = 120. L + 29 = 120. Subtract 29 from both sides. L = 91.