SOLUTION: The difference of two numbers is 6. The sum of 2 times the larger number and 3 times the smaller number is 37. Find the two numbers.

Question 886649: The difference of two numbers is 6. The sum of 2 times the larger number and 3 times the smaller number is 37. Find the two numbers.
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
A - B = 6, which also means that A = B + 6
2A + 3B = 37
Take the value of A from the first equation and plug it in to the second.
2A + 3B = 37
2(B+6) + 3B = 37
Distribute
2B + 12 + 3B = 37
Add
5B + 12 = 37
Subtract 12 from each side
5B = 25
Divide each side by 5
B = 5
.
If B is 5 and the difference between A and B is 6, then A = 11
.
2A + 3B = 37
(2*11) + (3*5) = 37
22 + 15 = 37
37 = 37
Success!
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