amount invested in each?

Question

Fran receives $274 per year in simple interest from investing

​$3200. Part is invested at​ 7%, part at​ 8% and part at​ 9%. There is $1000 more invested at​ 9% than at​ 8%. Find the amount invested at each rate.

Answer 1

3200 invested in all.

Let’s denote x to be the amount invested at 8%.

This gives us three different amounts invested all in terms of x.

.08(x)+ 0.09(x +1000) + 0.07(3200 - (x) - (x +1000)) = 274

Doing the addition gives us:

0.08x + 0.09x + 90 + 224 - 0.07x - 0.07x - 70 = 274

This is all simplified to 0.03x + 244 = 274 then

0.03x = 30

This means x is 1000. x + 1000 is 2000 which is amount invested at 9%. Then the amount invested at 7% is 200.