SOLUTION: 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

Algebra ->  Finance -> SOLUTION: 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       Log On


   

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!
Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
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% = %28-+700%29%2F-+0.07, or $highlight_green%2810000%29

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

E, or amount invested at 5% = %28-+60%29%2F-+.005, or $highlight_green%2812000%29

Amount invested at 5.5%: 40,000 – (10,000 + 12,000), or 40,000 – 22,000, or $highlight_green%2818000%29

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