Question 1149106
let x = the interest rate for investment P.
let y = the interest rate for investment Q.


you get:


3000x + 2000y = 640
2000x + 3000y = 660


multiply both sides of the first equation by 2 and multiply both sides of the second equation by 3 to get:
6000x + 4000y = 1280
6000x + 9000y = 1980
subtract the first equation from the second to get:
5000y = 700
solve for y to get:
y = .14
replace y with .14 in the first original equation to get:
3000x + 2000y = 640 becomes 3000x + 2000*.14 = 640 which becomes 3000x + 280 = 640.
subtract 280 from both sides of this equation to get:
3000x = 640 - 280 which becomes 3000x = 360.
solve for x to get x = 360/3000 = .12
you have x = .12 and y = .14
go back to your two original equations and replace x with .12 and y with .14 to get:
3000x + 2000y = 640 becomes 3000*.12 + 2000*.14 = 640 which becomes 360 + 280 = 640 which becomes 640 = 640 which is true.
2000x + 3000y = 660 becomes 2000*.12 + 3000*.14 = 660 which becomes 240 + 420 = 660 which becomes 660 = 660 which is true.
both original equations are true when x = .12 and y = .14.
x% = x * 100 = 12%
y% = y * 100 = 14%.
since they asked for the value of x and y, and not for the value of x% and y%, your solution is x = .12 and y = .14.
if the man has put all 5000 in bank Q, then he would have earned interest of 5000 * .14 = 700.