Question 982515
 Channing derives an income of P618 from some money invested at 3% and some at 4.5% if the amounts of the respective investments were interchanged, he would receive P336.
 How much did he originally invest at each rate?
;
let x = amt of 1st investment
let y = amt of 2nd investment
:
Write an equation for each scenario
.045x + .03y = 636
.03x + .045y = 618
:
Rearrange the 1st equation
.03y = -.045x + 636
divide both sides by .03
y = {{{-.045/.03}}}x + {{{636/.03}}}
y = -1.5x + 21200
:
Replace y with (-1.5x+21200) in the 2nd equation
.03x + .045(-1.5x+21200) = 618
.03x - .0675x + 954 = 618
.03x - .0675x = 618 - 954
-.0375x = -336
x = {{{(-336)/(-.0375)}}}
x = $8960 amt in the 1st investment
then
y = -1.5(8960) + 21200
y = -13440 + 21200
y = $7760 amt in the 2nd investment
:
:
You can check this for yourself:
 .03(8960) + .045(7760) =
and
 .045(8960) + .03(7760) =