Question 1111648
x equals the amount invested at 6%.
x + 1000 equals the amount invested at 8%.


the interest on the amount invested at 8% is 500 more than the interest on the amount invested at 6%.


the equation for that is:


.08 * (x + 1000) = .06 * x + 500


simplify to get .08 * x +  80 = .06 * x + 500


subtract .06 * x from both sides of this equation and subtract 80 from both sides of this equation to get:


.02 * x = 420


divide both sides of this equation by .02 to get:


x = 420 / .02 = 21,000


go back to your original equation and replace x with 21,000.


the original equation is .08 * (x + 1000) = .06 * x + 500


replace x with 21,000 to get:


.08 * 22,000) = .06 * 21,000 + 500


simplify to get:


1,760 = 1,760, which is true.


.08 * 22,000 = 1,760
.06 * 21,000 = 1,260


the difference is 500, as stated in the problem statement.


the solution is:


21,000 was invested at 6% and 22,000 was invested at 8%.