SOLUTION: Billy invests $12,000. Part of it at 4% intrest and the rest at 5.5%. If his interest was $532.50 how much did he invest at each rate?

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Question 353616: Billy invests $12,000. Part of it at 4% intrest and the rest at 5.5%. If his interest was $532.50 how much did he invest at each rate?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
all these money type problems are set up the same way once u get used to seeing the pattern then you wont have trouble figuring out what needs to be done


total=$12000
to get total add both portions x+y
so x%2By=12000
4%=.04 and 5.5%=.055
the total interest amount is $532.50
so.04x%2B.055y=532.5


So you have now found your 2 equations to bea ble to solve this problem, once you get used to doing these this process to finding the equations will come naturally.
x%2By=12000
.04x%2B.055y=532.5


You can solve by elimination or by substitution whichever you find more comfortable using, I like Elimination method as it is much faster.
x%2By=12000 multiply by .055
.04x%2B.055y=532.5
.
.055x%2B.055y=660
.04x%2B.055y=532.5 subtract equations
-------------------------
.015x=127.5 divide by .015
highlight%28x=8500%29 this is the portion at 4% interest


Now instead of doing that whole process over to find "y" simply plug in the value of "x" in the equation x%2By=12000
%288500%29%2By=12000
highlight%28y=3500%29 this is the portion at 5.5% interest