document.write( "Question 1185278: A bank loaned out $19,500, part of it at the rate of 4% annual interest, and the rest at 5% annual interest. The total interest earned for both loans was $940.00. How much was loaned at each rate \n" ); document.write( "

Algebra.Com's Answer #816078 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "If you need to solve 2-part \"mixture\" problems like this often, and a formal algebraic solution is not required, here is a quick and easy way to solve this kind of problem.

\n" ); document.write( "(1) All $19,500 at 4% would yield $780 interest; all at 5% would yield $975 interest. The actual interest was $940.
\n" ); document.write( "(2) Picture the three interest amounts on a number line -- 780, 940, and 975 -- and observe/calculate that 940 is 160/195 of the way from 780 to 975. That means 160/195 of the total amount was invested at the higher rate.
\n" ); document.write( "(3) The numbers work out very nicely in this example; 160/195 of $19,500 is $16,000.

\n" ); document.write( "ANSWER: $16,000 was invested at 5%; the other $3,500 at 4%.

\n" ); document.write( "CHECK: .05(16000)+.04(3500)= 800+140=940

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