Select the set of equations that represents the following situation: Mike invested $240 for one year. He in

Select the set of equations that represents the following situation: Mike invested $240 for one year. He invested part of it at 9% and the rest at 10%. At the end of the year he earned $23.42 in interest. How much did Mike invest at each rate of interest?

x + y = 240; 0.09x + 0.10y = 23.42
0.09 • 240 + 0.10 • 240 = 23.42
0.09x + 0.10y = 240; x + y = 23.42
x + y = 240; 9x + 10y = 23.42

Let the amount invested at 9% be x, and the amount invested at 10% be y. then x + y = 240.
The formula for simple interest is I = PRT/100 (I = Interest, P = Principal, R = interest rate, T = Time)
Note T = 1 (year)
then, 23.42 = x9/100 + y10/100.............Equation (1)
23.42 = 0.09x + 0.10y.........and, of course x + y = 240......so the first option is correct.

As y = 240 - x, Equation (1) becomes : 23.42 = 9x/100 + 10(240 - x)/100
2342 = 9x + 2400 - 10x
x = 2400 - 2342 = 58..........which means that y = 240 - 58 = 182
Then MIke invested $58 at 9% and $182 at 10%.