An investor has $12,000 to invest. He invests some of the money at an annual interest rate of 6% and the rest at 10%, such that he earns a return of $1040 after

Question

such that he earns a return of $1040 after the first year. construct and solve a system of linear equation to find out how much he invests at each rate. thank you need help with how to setit up ans solve.

Answer 1

Let x be the amount invested at 6% and y be the amount invested at 10%.

 

One equation states that the total invested is $12,000

x + y = 12,000

 

Another equation states that the interest earned is $1040

 

0.06x + 0.10y = 1040

 

Multiplying the second equation by -10 gives

 

-0.6x - y = -10,400

 

Adding this to the first equation eliminates y and gives

 

0.4x = 1600

x = 4000

 

Substituting 4000 for x into the first equation gives

 

4000 + y = 12,000

y = 8000