Question

A college student earned $8200 during summer vacation working as a waiter in a restaurant on the boardwalk at the beach. The student invested part of the money at 7% and the rest at 10%. If the student received a total of $664 in interest at the end of the year, how much was invested at 10%

Answer 1

$3000.

Explanation:

Suppose the amount invested at 7% is $X and the amount invested at 10% is $Y (assuming that the college student invested all his/her income on the two schemes). Therefore:

X + Y = 8200 (The sum of investments is basically the total income).

0.07X + 0.1Y = 664 (The sum of the interest received from the invested amounts is actually the total return).

Now solving these 2 simultaneous equations:

x + y = 8200 (Equation 1)

7x + 10y = 66400 (Equation 2)

From (Equation 1):

x = 8200 - y (Equation 3)

Put (Equation 3) in (Equation 2):

7(8200 - y) + 10y = 66400.

57400 - 7y + 10y = 66400.

3y = 9000

y = 3000.

$Y is the amount invested at 10%, therefore the final answer is $3000!!!