An investment of $29,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 2250. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment.
Accepted Solution
A:
Answer:The amounts of three parts of the investment are 18000, 6000, 5000 respectively.Step-by-step explanation:An investment of $29,000 was made by a business club.Let the amount of first and second investment be x and y respectively. So, the amount of third investment is (29000-x-y).The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 2250.[tex]0.08x+0.06y+0.09(29000-x-y)=2250[/tex]On simplification we get[tex]-0.01x-0.03y+2610=2250[/tex][tex]-0.01x-0.03y=2250-2610[/tex][tex]-0.01x-0.03y=-360[/tex][tex]0.01x+0.03y=360[/tex] ..... (1)The interest from the first investment was 4 times the interest from the second.[tex]0.08x=4(0.06y)[/tex][tex]0.08x=0.24y[/tex][tex]x=3y[/tex] .... (2)From (1) and (2) we get[tex]0.01(3y)+0.03y=360[/tex][tex]0.03y+0.03y=360[/tex][tex]0.06y=360[/tex]Divide both sides by 0.06.[tex]y=6000[/tex]Put this value in equation (2).[tex]x=3(6000)=18000[/tex] The amount of third investment is[tex]29000-x-y=29000-18000-6000=5000[/tex]Therefore the amounts of three parts of the investment are 18000, 6000, 5000 respectively.