Question

A bank loaned out ​$16000​, part of it at the rate of 7% per year and the rest at 15% per year. If the interest received in one year totaled ​$1500​, how much was loaned at 7 % question mark How much of the ​$16000 did the bank loan out at 7 % question mark

Answer 1

$11,250

Explanation:

Normally, when I work "mixture" problems, I like to choose the variable so it represents the amount of the largest contributor. Here, that would be the amount invested at 15%.

Unfortunately, the question asks for the amount invested at 7%. Using a variable to represent that amount means that there will be negative numbers involved. Care must be taken in the arithmetic.

Let x represent the amount invested at 7%. Then 16000-x is the amount invested at 15%. The total interest for one year is ...

0.07x + 0.15(16000 -x) = 1500 . . . . sum of interest amounts at each rate

-0.08x +2400 = 1500 . . simplify

-0.08x = -900 . . . . . . . . subtract 2400

x = 11250 . . . . . . . . . . . . divide by -0.08

The bank loaned $11,250 at 7%.