SOLUTION: 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 o

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 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 o      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
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)