SOLUTION: The sum of two numbers is 15. Twice one number equoals three times the other. Find the numbers.

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Question 119871: The sum of two numbers is 15. Twice one number equoals three times the other. Find the numbers.
Found 2 solutions by Earlsdon, josmiceli:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be x and y.
x%2By+=+15 and...
2x+=+3y rewrite this as: x+=+%283%2F2%29y and substitute into the first equation.
%283%2F2%29y%2By+=+15 Combine like-terms.
%285%2F2%29y+=+15 Multiply both sides by the multiplicative inverse of 5%2F2 which is 2%2F5.
y+=+6
x+=+%283%2F2%29y
x+=+%283%2F2%29%286%29
x+=+9
Check:
x%2By+=+15 Substitute x = 9 and y = 6.
9%2B6+=+15
15+=+15 OK, and...
2x+=+3y
2%289%29+=+3%286%29
18+=+18 OK

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the numbers x and y
x+%2B+y+=+15
2x+=+3y
x+=+%283%2F2%29%2Ay
%283%2F2%29y+%2B+y+=+15
%285%2F2%29y+=+15
y+=+%282%2F5%29%2A15
y+=+6
x+%2B+y+=+15
x+%2B+6+=+15
x+=+9
The numbers are 6 and 9
check:
2x+=+3y
2%2A9+=+3%2A6
18+=+18
OK