SOLUTION: The sum of two integers is twenty-four. The difference between four times the smaller integer and nine is three less than twice the larger integer. Find the integers.

Question 713394: The sum of two integers is twenty-four. The difference between four times the smaller integer and nine is three less than twice the larger integer. Find the integers.

Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
,
and
if , then .

Hard to know if 4x-9 is positive or negative. Lets first assume it's positive. We could then say 4x-9=2y-3 and then
4x-2y=9-3
4x-2y=6
2x-y=3

Will this condition continue to work?
From first equation, x=24-y.
2(24-y)-y=3
48-2y-y=3
48-3y=3
48-3=3y
45=3y
y=15.

Now we still want to find x, and remember, we must use .
Based on x=24-y, x=24-15, x=9. Good! This worked.

Final Answer: x=9 and y=15.
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