SOLUTION: A, B, & C have equal incomes from investments. A has invested $2000 less than B and $2500 more than C . The rate of interest received by A is 1 per cent more than that received by

Question 578502: A, B, & C have equal incomes from investments. A has invested $2000 less than B and $2500 more than C . The rate of interest received by A is 1 per cent more than that received by B and 2 per cent less than that received by C. How much has A invested? Pls. help me solve this. I've been working on it for 2 hours now and still can't come up with the equation and the answer. Thanks.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A, B, & C have equal incomes from investments.
A has invested $2000 less than B and $2500 more than C .
The rate of interest received by A is 1 per cent more than that received by B
and 2 per cent less than that received by C.
How much has A invested?
:
You're right, this is a doozy
:
Let A, B, C = amt of each investment
Let a, b, c = interest rate of each in decimal form
:
Given that incomes are equal:
aA = bB = cC
Write an equation for each statement:
:
Get B and C in terms of A, and get b & c in terms of a
:
" A has invested $2000 less than B."
A = B-2000
or
B = (A+2000)
and
"$2500 more than C"
A = C+2500
or
C = (A-2500)
:
" The rate of interest received by A is 1 per cent more than that received by B"
a = b+.01
or
b =(a-.01)
:
"and 2 per cent less than that received by C."
a = c-.02
or
c = (a+.02)
:
We know
aA = bB
replace b with (a-.01) and B with (A+2000)
aA = (a-.01)(A+2000)
FOIL the right
aA = aA + 2000a - .01A - 20
Subtract aA from both sides, add 20 to each side
2000a - .01A = 20
:
aA = cC
replace c with (a+.02) and C with (A-2500)
aA = (a+.02)(A-2500)
FOIL the right
aA = aA - 2500a + .02A - 50
Subtract aA from both sides, add 50 to each side
-2500a + .02A = 50
:
Use elimination with these two equation, multiply the 1st on by 2, add to the 2nd
4000a - .02A = 40
-2500a +.20A = 50
-------------------adding eliminates A, find a
1500a = 90
a =
a = .06, so 6% is the int rate of the A investment
then
b = .06 - .01
b = .05, 5% is the int rate of the B investment
and
c = .06 +.02
c = .08, 8% is the int rate of the C investment
:
Remember aA = bB
.06A = .05B
Replace B with (B+2000)
.06A = .05(A+2000)
.06A = .05A + 100
.06A - .05A = 100
.01A = 100
A =
A = $10,000 investment which is what they want
:
:
You can check this by finding the actual interest from B & C, confirming that they are all equal. I did this and found each had a return of $600, but don't take my word for it. C

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