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?

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) (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)

RELATED QUESTIONS
Find two numbers whose sum is 163 such that when the larger number is divided by the... (answered by KMST)

find two numbers whose some is 163 such that when the larger number is divided by the... (answered by lwsshak3)

The sum of two numbers is 17. When the larger is divided by the smaller the quotient is 3 (answered by solver91311)

The sum of two numbers is 17. When the larger is divided by the smaller the quotient is 3 (answered by josmiceli)

the sum of two number is 36. if the larger is divided by the smaller the quotient is 2... (answered by josgarithmetic,god2012)

Two positive numbers differ by 11. when the larger number divided by the smaller number,... (answered by josgarithmetic)

Two numbers differ by 11. When the larger number is divided by the smaller, the quotient... (answered by robertb)

the sum of two numbers is 30. if the larger number is divided by the smaller number the... (answered by Stitch)

The sum of the two numbers is 54. If the larger is divided by the smaller, the quotient... (answered by ankor@dixie-net.com)