SOLUTION: Find two numbers whose sum is 143 such that when the larger number is divided by the smaller, the quotient is 3. and the remainder is 3. What are the numbers?

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Question 652539: Find two numbers whose sum is 143 such that when the larger number is divided by the smaller, the quotient is 3. and the remainder is 3. What are the numbers?
Answer by Shana-D77(132) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start by translating the problem from words to math. Since there is a large and small number, let's say that:
x = large number
y = small number
"Find two numbers whose sum is 143"
x + y = 143 (we'll call this "easier original equation")
"Such that when the larger number is divided by the smaller, the quotient is 3. and the remainder is 3."
x/y = 3 + 3/y (the 3/y part means "remainder of 3" when the divisor is y)
x/y = 3y/y + 3/y (multiplied that lonely 3 by y/y so that I can make the denominators the same, so that I can...
x/y = (3y + 3)/y (... put all of the left side over y. This cleans things up a bit)
Now both sides are being divided by y, so we can mentally multiply both sides by y and get:
x = 3y + 3
Our "easier original equation" was x + y = 143. Solved for x to match the x = 3y + 3 we just got, we have the two equations:
x = 3y + 3
x = 143 - y
Since they're both =x, we can set them equal to each other (transitive property):
3y + 3 = 143 - y
4y + 3 = 143 (added y to both sides)
4y = 140 (subtracted 3 from both sides)
y = 35.
If y = 35, then x = 143 - 35:
x = 108
(108, 35)