An executive invests $28,000, some at 5% and some at 4% annual interest. If he receives an annual return of $1,260, how much is invested at each rate?

Question

 college math question that I cannot solve. 

Answer 1

This is a system of two equations. You have some amount of money, let's call it X, that is invested at 5% interest, and some other amount of money, let's call it Y, that is invested at 4% interest. You know that together X and Y sum to a $28,000 total investment, and that their gained interest sums to a total of $1,260. So we can write this down mathematically as:

 

X + Y = 28,000

.05X + .04Y = 1,260

 

From here you can use your preferred method of solving a system of two equations (substitution, elimination, or row-reducing a matrix would be some options). You end up with the somewhat surprisingly simple answer of X = 14,000 and Y = 14,000.

Answer 2

The simplest solution.  Let x be the amount invested at 4%.  Then, since 28000 is invested, 28000 - x is invested at 5%.

Thus, the return is .04 x + .05 (28000 - x);

The return is 1260, so

.04 x + .05 (28000 - x) = 1260

.04x + 1400 - .05x = 1260

-.01x = -140

x = 14000

2800 - 14000 = 14000

14000 is invested at both 4% and 5%.