Question 288546
Jed and Sam each have $X to invest. Jed invests part of his money in an investment account at
the bank at 10% p.a. interest and the rest in shares at 12.5% per annum. At the end of the year
Jed receives an income of $1625 from his investments. Sam invests twice as much as Jed in
shares at 12.5% and puts the rest into an investment account at 8% p.a. At the end of the year
Sam receives an income of $1650 from his investments. How much did each person originally
have to invest?

let Jed invest y amount @ 12.5% 

he will invest x-y at 10%

12.5/100 y + 10/100(x-y)=1625

12.5 y + 10(x-y)= 1625*100

12.5y + 10x -10y = 162500

2.5y +10x = 162500-------------  1


Sam invests 2y at 12%

The rest he invests at 8% ie: x-2y

12.5/100 *2y + 8/100*(x-2y)=1650

25y +8(x-2y) = 1650 *100

25y +8x-16y= 165000-------------2


2.5y +10x = 162500-------------  1
9y +8x  = 165000--------------2

multiply eq 1 by 8 and eq 2 by 10


20y +80x = 1300000

90y +80x = 1650000

-70y=-350000

y= -350000/-70

= 5000

Jed invest $5000 at 12.5%

plug the value of y in eq. 1 

x= 15000 the amount invested by Jed at 8%

Sam ivests 2y at12.5 %  =10000

Sam invests $15000 at 8% ( plug the value of y in eq 2)