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

  $11,250

Step-by-step 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%.