Question

To buy both a new car and a new house, Tina sought two loans totaling $319,531. The simple interest rate on the first loan was 2.7%, while the simple interest rate on the second loan was 2.6%. At the end of the first year, Tina paid a combined interest payment of $8334.15. What were the amounts of the two loans?

Answer 1

the first equation is:
x + y = 319,531
the second equation is:
.027*x + .026*y = 8334.15
x is the loan that requires 2.7% interest.
y is the loan that requires 2.6% interest.
the 2 equations that need to be solved simultaneously are:
x + y = 319,531
.027*x + .026*y = 8334.15
we can solve for x in the first equation to get:
x = 319,531 - y
we can substitute for x in the second equation to get:
.027*(319,531-y) + .026*y = 8334.15
when solve for y :

simplify the equation to get:
.027*319,531 - .027*y + .026*y = 8334.15
simplify further to get:
8627.337 - .027*y + .026*y = 8334.15
combine like terms to get:
8627.337 - .001*y = 8334.15
add .001*y to both sides of the equation and subtract 8334.15 from both sides of the equation to get:
8627.337 - 8334.15 = .001*y
combine like terms to get:
293.187 = .001*y
divide both sides of the equation by .001 to get:
293,187 = y
since x + y = 319,531, this means that x = 319,531 - 293,187 = 26,344.
You get: x = 26,344
y = 293,187
you get: .027*x = 711.288
.026*y = 7622.862
You get: x + y = 319,531
You get: .027*x + .026*y = 8334.15