# SOLUTION: 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 lo

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 Question 480176: 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 year, Tina paid a combined interest payment of \$8334.15. What were the amounts of the two loans?Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!2 loans totaled 319,531. first loan interest is 2.7% simple. second loan interest is 2.6% simple. combine interest payment at end of first year is 8334.15 amounts of the 2 loans were what? ----- we have 2 equations that need to be solved simultaneously to get your answer. 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 we solve for y as follows: 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. we have: x = 26,344 y = 293,187 we have: .027*x = 711.288 .026*y = 7622.862 we have: x + y = 319,531 we have: .027*x + .026*y = 8334.15 the numbers check out so we're good.