SOLUTION: write an equation and solve An investor has $7500 invested at one rate and $6200 invested at a different rate. If the second investment is at a rate 2% lower than the first, fin

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: write an equation and solve An investor has $7500 invested at one rate and $6200 invested at a different rate. If the second investment is at a rate 2% lower than the first, fin      Log On


   

Question 992431: write an equation and solve
An investor has $7500 invested at one rate and $6200 invested at a different rate. If the second investment is at a rate 2% lower than the first, find the rate for each investment if his combined annual interest income is $698.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
rate is equal to percent / 100.
2% is therefore equal to a rate of .02.

x is the rate that 7500 is invested at.
x - .02 is the rate that 6200 is invested at.

your equation is:

7500 * x + 6200 * (x-.02) = 698

simplify to get:

7500 * x + 6200 * x - .02 * 6200 = 698

simplify further to get:

(7500 + 6200) * x - 124 = 698

subtract 124 from both sides of the equation and simplify further to get:

13700 * x = 822.

divide both sides of the equation by 13700 to get:

x = 822 / 13700 = .06

x - .02 = .06 - .02 = .04

7500 was invested at 6% and 6200 was invested at 4%.

7500 * .06 + 6200 * .04 = 450 + 248 = 698.

your solution is that the rate for 7500 is 6% and the rate for 6200 is 4%.