SOLUTION: I don't understand how to solve this complicated linear equation word problem. I would really appreciate if you could help me out, thanks. THE SUM OF TWO NUMBERS IS 36. IF THE L

Question 91629: I don't understand how to solve this complicated linear equation word problem. I would really appreciate if you could help me out, thanks.
THE SUM OF TWO NUMBERS IS 36. IF THE LARGER NUMBER IS DIVIDED BY THE SMALLER NUMBER, THE QUOTIENT IS 2 AND THE REMAINDER IS 3. FIND THE NUMBERS.
I'm sorry but this isn't a textbook question
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let's begin by calling the smaller number S and the larger number L.
.
The problem tells you that the sum of these two numbers is 36. Therefore, we can write the
equation:
.
<=== first equation
.
The the problem tells you to divide the larger number by the smaller number. In algebraic
form this would be
.
Furthermore it tells you that the result of this division equals 2 plus a remainder of

.
So the equation form of this division is:
.
<=== second equation
.
If we return to the first equation and subtract S from both sides, we get:
.

.
Since L equals 36 - S we can substitute 36 - S for L in the second equation which then
becomes:
.

.
Notice that if we say the first term on the right side (that term is 2) is equivalent to
then we can substitute for 2 and every term in the equation will
then have an S in the denominator and the equation will be:
.

.
We can now get rid of the S in the denominator by multiplying all terms on both sides by S
to get:
.

.
Now add S to both sides of the equation to get rid of the -S on the left side. The equation
then becomes:
.

.
Then subtract 3 from both sides to get rid of the 3 on the right side. The equation
then becomes:
.

.
Finally, divide both sides by 3 to solve for S:
.

.
So now we know the smaller number is 11. But since the sum of the two numbers is 36, then
the larger number must be 25 because 36 - 11 = 25.
.
So the two numbers are 11 and 25.
.
Check: is their sum 36? Yes it is.
.
If you divide the larger (25) by the smaller (11) do you get an answer of 2 with a remainder
of 3? Yes you do. Our answer checks ... the smaller number is 11 and the larger number is 25.
.
Hope this helps you to see your way through the problem.
.

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