SOLUTION: The difference between two numbers is 5. The sum of four times the smaller and the larger is 35. Find the numbers.

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Question 549025: The difference between two numbers is 5. The sum of four times the smaller and the larger is 35. Find the numbers.
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
Lets call our two numbers x (the smaller number) and y (the larger number) (in general, whenever you are given a word problem, let some variable represent what you are looking for).
From the question we can get the following equations:
y-x=5 (1)
and
4x%2By=35 (2)
Rearranging (1) we get:
y=5%2Bx (3)

Now substitute (3) into (2) to get:
4x%2B5%2Bx=35
5x%2B5=35
5x%2B5-5=35-5
5x=30
5x%2F5=30%2F5
x=6
Now substitute this value for x back into (3) to find our y
y=6%2B6
y=12

So our bigger number is 12 and our smaller number is 6.