Question 1153985

An investment of ​$70 comma 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 $ 5220. The interest from the first investment was 2 times the interest from the second. Find the amounts of the three parts of the investment.

The first part of the investment was ​$

2nd part $

Third part $
<pre>Let amount invested at 8% and 6% be E, and S, respectively
Then amount invested at 9% = 70,000 - E - S
We then have: .08E + .06S + .09(70,000 - E - S) = 5,220
.08E + .06S + 6,300 - .09E - .09S = 5,220
- .01E - .03S = - 1,080 ------ eq (i)

Also, {{{matrix(1,14, .08E, "=", 2(.06S), "=====>", E, "=", 2(.06)/.08, "====>", E, "=", 1.5S, "------", eq, "(ii)")}}}
- .01(1.5S) - .03S = - 1,080 ------- Substituting 1.5S for E in eq (i)
- .015S - .03S = - 1,080
- .045S = - 1,080
S, or amount invested at 6% = {{{highlight_green(matrix(1,3, ("- 1,080")/(- .045), "=", "$24,000"))}}} 
Now you can find the amounts invested at 6% and 9%.