SOLUTION: the difference of two integers is 9. five times the smaller is 9 more than three times the larger. find the integers.

Question 831092: the difference of two integers is 9. five times the smaller is 9 more than three times the larger. find the integers.

Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
Let A be the larger integer, and B be the smaller integer.
A - 9 = B
5B = 3A + 9
Multiply the top equation by 5 to make it easier to work with.
5A - 45 = 5B
Substitute the values from the top equation into the bottom
(5A - 45) [this WAS 5B in the equation] = 3A + 9
5A - 45 = 3A + 9
Subtract 3A from each side
2A - 45 = 9
Add 45 to each side
2A = 54
Divide each side by 2
A = 27 <<--
.
Let's make sure it's right by putting it back into the original question.
"the difference of two integers is 9." Therefore, B = 27-9, or 18. <<--
"five times the smaller is 9 more than three times the larger" (5*18) = (3*27) +9
90 = 81 + 9
90 = 90
Success!
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