SOLUTION: A bank loaned out ​$14,000​, part of it at the rate of 6% per year and the rest at 16% per year. If the interest received in one year totaled ​1500$​, how much was loaned a

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Question 1185811: A bank loaned out ​$14,000​, part of it at the rate of 6% per year and the rest at 16% per year. If the interest received in one year totaled ​1500$​, how much was loaned at 6%
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A standard "mixture" problem....

First a standard setup for solving the problem using algebra.

x dollars at 6%, plus (14000-x) dollars at 16%, yields $1500 interest.



Solve using basic algebra, although the numbers are a bit messy.

And now a quick and easy way to solve any 2-part mixture problem like this, if a formal algebraic solution is not required and your mental math skills are good.

$14,000 all invested at 6% would yield $840 interest; all at 16% would yield $2240 interest; the actual interest was $1500.

Picture the three interest amounts -- 840, 1500, and 2240 -- on a number line and observe/calculate that 1500 is 660/1400 of the way from 840 to 2240. That means 660/1400 of the total was loaned at the higher rate.



ANSWER: $6600 was loaned at 16%; the other $7400 at 6%.

CHECK: .16(6600)+.06(7400)=1056+444=1500


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