Question

Nico is saving money for his college education. He invests some money at 9​%, and ​$1700 less than that amount at 5%. The investments produced a total of ​$223 interest in 1 yr. How much did he invest at each​ rate?

He invested $___ at 9% and $___ at 5%.

Answer 1

Let
`x_1` the amount of money invested at 9% and
`x_2` the amount of money invested at 5%. The amount invested at 5% (
`x_2`) is 1700$ less than the amount invested at 9% (
`x_1`) it means:

`x_1 - 1700 = x_2` (equation 1)
The investments produced 223$ which means:

`(9)/(100) x_1 + (5)/(100) x_2 = 223`. (equation 2)
We use the first equation to eliminate
`x_2` from equation 2:

`(9)/(100) x_1 + (5)/(100) (x_1-1700) - = 223\\ (9)/(100) x_1 + (5)/(100) x_1- (5)/(100)1700 - = 223\\ (14)/(100) x_1 = 308\\ X_1 = 308*(100)/(14) = 2200\\ X_2 = X_1-1700 = 2200-1700 = 500`

He invested 2200$ at 9% and 500$ at 5%.