SOLUTION: a person invests $20000, partly at 5%, partly at 6% and the remainder at 6.5%. the total annual interest is $1170. three times the amount invested at 6% is equals the amount invest
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Question 1109146: a person invests $20000, partly at 5%, partly at 6% and the remainder at 6.5%. the total annual interest is $1170. three times the amount invested at 6% is equals the amount invested at 5% and 6.5% combined. how much money is invested at each rate
Found 2 solutions by josmiceli, TeachMath:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = amount invested @ 5%
Let = amount invested @ 6%
Let = amount invested @ 6.5%
----------------------------------
(1)
(2)
(3)
(4)
(5)
(6)
----------------------------------
There are 6 equations and 6 unknowns,
so it's solvable
-------------------
Plug (6) into (5)
(5)
(5)
(5)
-----------------------------
Plug this result into (2)
(2)
(2)
------------------------------
Plug this result back into (6)
(6)
-----------------------------
and from (1), (2), and (3)
Multiply both sides of (6) by
and subtract (6) from this result
--------------------------------
and
(5)
(5)
(5)
I think you can finish from here
Definitely check the math.
I think the method good, though
Answer by TeachMath(96) (Show Source): You can put this solution on YOUR website!
You can use just 2 variables. Using more can make the problem a lot more complex, in my opinion.
Let amount invested at 5% and 6.5% be F and S, respectively
Then amount invested at 6% = 20,000 – F – S
We then get: .05F + .065S + .06(20,000 – F – S) = 1,170
.05F + .065S + 1,200 - .06F - .06S = 1,170
- .01F + .005S = - 30 ------- eq 1
Also, 3(20,000 – F – S) = F + S
60,000 – 3F - 3S = F + S
F + 3F + S + 3S = 60,000
4F + 4S = 60,000___4(F + S) = 4(15,000)____F + S = 15,000___S = 15,000 - F ---- eq 2
- .01F + .005(15,000 - F) = - 30 ------- Substituting 15,000 – F for S in eq 1
- .01F + 75 – .005F = - 30
- .01F - .005F = - 30 - 75
- .015F = - 105
F, or amount invested at 5% = - 105/- .015 = $7,000
S = 15,000 – 7,000 ------- Substituting 7,000 for F in eq 2
S, or amount invested at 6.5% = $8,000
Amount invested at 6%: 20,000 – 7,000 – 8,000 = $5,000
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