Question 1185199
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.