Question 1072679
let y = the investment.


let x = the lower interest rate.


the higher interest rate is 2% more than the lower interest rate.


that makes the higher interest rate equal to x + .02


the interest using the lower interest rate is 315.


the interest using the higher interest rate is 405.


you get:


y * x = 315


y * (x + .02) = 405


subtract the first equation from the second to get:


y * (x + .02) - y * x = 405 - 315


simplify to get:


y * x + .02 * y - y * x = 405 - 315


combine like terms to get:


.02 * y = 90


solve for y to get y = 90 / .02 = 4500.


this makes the investment equal to 4500.


now that you know y, you can solve for x.


the first equation is y * x = 315


replace y with 4500 and you get 4500 * x = 315


solve for x to get x = 315 / 4500 = .07


that's the smaller rate.


the larger rate is .02 more than that.


this makes the larger rate = .09


4500 * .07 = 315


4500 * .09 = 405


solution is confirmed to be good.