How would I go about solving this problem?

Question

Sierra invested her savings of $4800, part at 9% and the rest at 10% (both simple interest). At the end of the year the interest from the 9% investment was $43 less than the interest from the 10% investment. How much was invested at each rate?

Answer 1

Invest half at each rate. That would be 240 interest at 10% and 216 at 9% with 24 less at 9%. to get 43 less means investing less than half at 9% and more than half at 10%, but not by that much

.09(4800-X) = .10(X) -43

9(48)-.09X =.1X - 43

.19X = 432+43 = 475

X = 475/.19 = $2500 invested at 10%

4800-2500 = $2300 invested at 9%