SOLUTION: Alan3354 got rid of 2 migraines for me tonight. I solved this one but I am curious if I set it up correctly. (sorry, studying for finals and want a 4.0). "John used 5 gallons of

Question 321955: Alan3354 got rid of 2 migraines for me tonight. I solved this one but I am curious if I set it up correctly. (sorry, studying for finals and want a 4.0).
"John used 5 gallons of BLUE paint and 8 gallons of WHITE paint on his house. Kim used only 3 gallons of BLUE, but 11 gallons of WHITE at the same price per gallon as John's paint. If John spent $197 and Kim spent $205, how much was the blue paint per gallon?
My solution was x=total value of blue/5(# of blue gallons)+(197-x)/8(# of white gallons)=197/13(total # of gallons).
x/5+(197-x)/8=197/13
Am I on the right track and is "Kim's" info totally insignificant here or is my brain fried far more than I'm willing to admit??
"Not feeling like an A student anymore"
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
John used 5 gallons of BLUE paint and 8 gallons of WHITE John spent $197
Kim used only 3 gallons of BLUE, but 11 gallons of WHITE Kim spent $205,
Let blue paint cost $x/gallon
Let White paint cost $y per gallon
..
John
5x+8y=197.......... equation 1
Kim
3x+11y=205......... equation 2
multiply equation 1 by 3 and equation2 by 5 to eliminate x
..
15x+24y=591
15x+55y=1025
Subtract
15x+24y-15x-55y=591-1025
-31y=-434
y=434/31
y=14 dollars - cost of white paint / gallon
plug the value of y in equation 1
5x+8*14=197
5x=197-112
5x=85
x=17 dollars the cost of blue paint -
One more migraine gone I suppose

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