1. ## investor

An investor has $10000 to invest in 3 types of bonds: short-term, intermediate-term and long-bond term. Short term bonds pay 4% annually, intermediate term bonds pay 6%, and long terms bonds pay 8%. The investor wishes to have a total annual return of$6700 on her investment, with equal amounts invested in intermediate and long term bonds. How much should she invest in each type?

2. Originally Posted by aeroflix
An investor has $10000 to invest in 3 types of bonds: short-term, intermediate-term and long-bond term. Short term bonds pay 4% annually, intermediate term bonds pay 6%, and long terms bonds pay 8%. The investor wishes to have a total annual return of$6700 on her investment, with equal amounts invested in intermediate and long term bonds. How much should she invest in each type?
Start by naming your variables: Let x bet the amount of money invested in short term bonds, y the amount of money invested in intermediate term bonds, z the amount of money invested in long term bonds.

"An investor has \$10000 to invest":
x+ y+ z= 10000.

"The investor wishes to h ave a total annual return on her investment."
The return on any one amount is the amount invested times the percentage return: .04x, .06y, and .08z for each so the total is .04x+ .06y+ .08z=6700.

"with equal amounts invested in intermediate and long term bonds": y= z.

You have three equations in the three unknowns x, y, z:
x+ y+ z= 10000
.04x+ .06y+ .08z= 6700
y= z.

Since y= z, you can replace z by y in the first two equations:
x+ y+ y= x+ 2y= 10000
.04x+ .06y+ .08y= .04x+ .14y= 6700

From x+ 2y= 10000, you can get x= 10000- 2y and replace that in the last equation:
.04(10000- 2y)+ .14y= 6700.

Solve that equation for y and then work back to find x and z.

Don't forget to write your final answer as a complete sentence. You can't just say x= ..., y=..., z= ... because whoever gave you this problem doesn't know what "x", "y", and "z" mean.