Question

Sharon recieved a $20,000 inheritance from her grandfather. She invested some of the money in an account earning 3% interest and the remaining amount in an account earning 2.5% annual interest. If the total annual interest earned is $575, how much is invested at each rate.​

Answer 1

$15,000 at 3%

$5,000 at 2.5%

Explanation:

let x = amount invested at 3%

y = amount invested at 2.5%

x + y = 20,000 Equation 1

0.03x + 0.025y = 575 multiply by 100

3x + 2.5y = 57,500 Equation 2

multiply Equation 1 by -3

-3(x + y = 20,000)

-3x - 3y = -60,000 Equation 3

Add Equations 2 and 3

3x + 2.5y = 57,500

-3x - 3y = -60,000

_______________

-0.5y = -2,500

y = 5,000

Substitute y = 5,000 to any of the equations to get x, i use equation 1

x + y = 20,000

x + 5000 = 20,000

x = 15,000

let check if our answer is correct

3% of 15,000 + 2.5% of 5,000 = $575

$450 + $125 = $575