Skippy has a total of 9000 to split between two investments

Skippy has a total of $9.000 to split between two investments One account offers 3% simple interest, and the other account offers 8%, simple Interest, for tax reasons, ha can only earn Interest the entire year, How much money should Skippy each account to earn $500 in interest for the year?

Solution

Let us assume that Skippy invests $ x in the account paying 3 % simple interest. Then Skippy invests $ 9000- x in the account paying 8 % simple interest. The annual interst on the two accounts are x * 3 % = 3x/100 = 0.03x and (9000- x) * 8% = 0.08(9000 -x). Since thetotal annual interest is $ 500, we have 0.03x + 0.08( 9000 - x) = 500. On multiplying both the sides by 100, we get 3x + 8(9000 - x) = 50000 or 3x + 72000 - 8x or, 3x - 8x = 50000 - 72000 or, - 5x x = - 22000 or, 5x = 22000 Therefore, x = 22000/5 = $ 4400. Then 9000 - x = 9000 - 4400 = 4600. Thus Skippy invests $ 4400 in the account paying 3 % interest and $ 4600 in the account paying 8 % interest.