SOLUTION: 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 mor

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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