document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #328908 by Theo(13342) $\"\"$ $\"About$

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2 loans totaled 319,531.
\n" ); document.write( "first loan interest is 2.7% simple.
\n" ); document.write( "second loan interest is 2.6% simple.
\n" ); document.write( "combine interest payment at end of first year is 8334.15
\n" ); document.write( "amounts of the 2 loans were what?
\n" ); document.write( "-----
\n" ); document.write( "we have 2 equations that need to be solved simultaneously to get your answer.
\n" ); document.write( "the first equation is:
\n" ); document.write( "x + y = 319,531
\n" ); document.write( "the second equation is:
\n" ); document.write( ".027*x + .026*y = 8334.15
\n" ); document.write( "-----
\n" ); document.write( "x is the loan that requires 2.7% interest.
\n" ); document.write( "y is the loan that requires 2.6% interest.
\n" ); document.write( "the 2 equations that need to be solved simultaneously are:
\n" ); document.write( "x + y = 319,531
\n" ); document.write( ".027*x + .026*y = 8334.15
\n" ); document.write( "-----
\n" ); document.write( "we can solve for x in the first equation to get:
\n" ); document.write( "x = 319,531 - y
\n" ); document.write( "we can substitute for x in the second equation to get:
\n" ); document.write( ".027*(319,531-y) + .026*y = 8334.15
\n" ); document.write( "we solve for y as follows:
\n" ); document.write( "simplify the equation to get:
\n" ); document.write( ".027*319,531 - .027*y + .026*y = 8334.15
\n" ); document.write( "simplify further to get:
\n" ); document.write( "8627.337 - .027*y + .026*y = 8334.15
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "8627.337 - .001*y = 8334.15
\n" ); document.write( "add .001*y to both sides of the equation and subtract 8334.15 from both sides of the equation to get:
\n" ); document.write( "8627.337 - 8334.15 = .001*y
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "293.187 = .001*y
\n" ); document.write( "divide both sides of the equation by .001 to get:
\n" ); document.write( "293,187 = y
\n" ); document.write( "since x + y = 319,531, this means that x = 319,531 - 293,187 = 26,344.
\n" ); document.write( "we have:
\n" ); document.write( "x = 26,344
\n" ); document.write( "y = 293,187
\n" ); document.write( "we have:
\n" ); document.write( ".027*x = 711.288
\n" ); document.write( ".026*y = 7622.862
\n" ); document.write( "we have:
\n" ); document.write( "x + y = 319,531
\n" ); document.write( "we have:
\n" ); document.write( ".027*x + .026*y = 8334.15
\n" ); document.write( "the numbers check out so we're good.
\n" ); document.write( " \n" ); document.write( "

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