SOLUTION: Find two numbers who sum is 30 so that 5 times the larger number decreased by three times the smaller number is 54. Please help!

Question 340986: Find two numbers who sum is 30 so that 5 times the larger number decreased by three times the smaller number is 54.
Please help!
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
Find two numbers who sum is 30 so that 5 times the larger number decreased by three times the smaller number is 54
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Let S=small number
Let L=large number
--
given
S+L=30
5L-3S=54
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S=30-L solve for one of the variables
5L-3(30-L)=54 subtitute into the other equation
--
5L-90+3L=54
8L-90=54
8L=144
L=144/8=18
==
and
==
validate
5L-3S=54
5(18)-3(12)=90-36=54 check
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