Question 764622
One year, Don invested a total of $40,000, part at 4%, part at 5%, and the rest at 5.5%. The amount of interest received on the investments was $1990. The interest received on the 5.5% investment was $590 more than the interest received on the 4% investment. How much was invested at each rate?

I am having trouble solving this problem. I keep getting thrown off by the extra %. Any help would be greatly appreciated! 


Let the amount invested at 4% be F, and amount invested at 5%, E
Then amount invested at 5.5% = 40,000 – (F + E), or 40,000 – F – E


Interest received on4%: .04F
Interest received on 5%: .05E
Interest received on 5.5%: .055(40,000 – F – E), or 2,200 - .055F - .055E


Since total interest received on all investments = 1,990, then: 
.04F + .05E + 2,200 - .055F - .055E = 1,990
.04F - .055F + .05E - .055E = 1,990 – 2,200 
- .015F - .005E = - 210 ----- eq (i)


Also, 2,200 - .055F - .055E = .04F + 590 
.04F + .055F + .055E = 2,200 - 590 
.095F + .055E = 1,610 ------ eq (ii)


We now have:
- .015F - .005E = - 210 ----- eq (i)
.095F + .055E = 1,610 ------- eq (ii) 
– 0.165F - .055E = - 2,310 ------ Multiplying eq (i) by 11 -------- eq (iii) 
– 0.07F = - 700 ------ Adding eqs (iii) & eq (ii)


F, or amount invested at 4% = {{{(- 700)/- 0.07}}}, or ${{{highlight_green(10000)}}} 


- 150 – .005E = - 210 ------ Substituting 10,000 for F in eq (i) 
– .005E = - 210 + 150 
– .005E = - 60


E, or amount invested at 5% = {{{(- 60)/- .005}}}, or ${{{highlight_green(12000)}}}


Amount invested at 5.5%: 40,000 – (10,000 + 12,000), or 40,000 – 22,000, or ${{{highlight_green(18000)}}}


You can do the check!! 


Further help is available, online or in-person, for a fee, obviously. Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com