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Question 1185199: between her home mortage, car loan, and credit card bill, deena is $117,000 in debt. Each month, Deeans credit card accumulates 1.5% interest, her car loan 1% interest and her mortage .8% interest. After one month, her total accumulated interest is $995.00. The interest on Deena's mortage was $680 more than the interest on her car loan. How much does she owe on her car loan?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let M = the mortage amount
let L = the car loan amount
let C = the credit card amount.
M + L + C = 117,000
.008M + .01L + .015C = 995
multiply both sides of the first equation by .015 and leave the second equation as is to get:
.015M + .015L + .015C = 1755
.008M + .01L + .015C = 995
subtract the second equation from the first to get:
.007M + .005L = 760
you are given that .0008M = .01L + 680
re-arrange this to get:
.008M - .01L = 680
your two equations to solve simultaneously are now:
.007M + .005L = 760
.008M - .01L = 680
multoiply both sides of the first equation by 2 and leave the second equation as is to g et:
.014M + .01L = 1520
.008M + .01L = 680
add the two equations together to get:
.022M = 2200
solve for M to get:
M = 100,000
this also makes .008M equal to 800
your two original equations of:
M + L + C = 117,000
.008M + .01L + .015C = 995
become:
100,000 + L + C = 117,000
800 + .01L + .015C = 995
subtract 100,000 from both sides of the first equation and subtract 800 from both sides of the second equation to get:
L + C = 17,000
.01L + .015C = 195
multiply both sides of the first equation by .015 and leave the second equation as is to get:
.015L + .015C = 255
.01L + .015C = 195
subtract the second equation from the first to get:
.005L = 60
solve for L to get:
L = 12,000
this lets C be equal to 5000 because 100,000 + 12,000 + 5,000 = 117,000
.008M + .01L + .015C becomes 800 + 120 + 75 = 995
numbers look good.
your solution is:
she owes 12,000 on the car loan.
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