I dont know how to solve this can anyone help me?

Question

Part of $3000 is invested at 12%, another part at 13%, and the remainder at 14%. The total yearly income from the three investments is $400. The sum of the amounts invested at 12% and 13% equals the amount invested at 14%. Determine how much is invested at each rate

Answer 1

x = amount at 12%

y = amount at 13%

z = amount at 14%

 

Given:

 

x + y + z = $3000

 

Interest earned:

 

0.12x + 0.13y + 0.14z = $400

 

Given:

 

x + y = z ⇒ x + y - z = 0

 

Solve a system of 3 linear equations in 3 unknowns x, y, and z:

x + y + z = 3000

0.12x + 0.13y + 0.14z = 400

x + y - z = 0

 

Solving by Cramer's rule, I got

 

x = $500 at 12%

y = $1000 at 13%

z = $1500 at 14%