Anne done dual investments totaling $21,000. One investment done her the 13% profit, though upon the alternative investment she took the 9% loss. If her net any year detriment was $196, how most was in any investment?
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{ 3 comments… read them below or add one }
“two investments totaling $21,000″
x+y = 21,000
“One investment made 13% profit, the other investment a 9% loss”
0.13x = profit
0.09y = loss
“net yearly loss was $196″
0.13x – 0.09y = -196
You now have a system of two linear equations for two unknowns:
x + y = 21,000
0.13x – 0.09y = -196
I don’t know how you go about solve systems of linear equations, but I got x = 7700, y = 13,300
Check:
0.13x – 0.09y = (0.13×7700) – (0.09×13,300
= 1001 – 1197
= -196
Let P be the investment that made a 13% profit
(profit = .13P)
Let L be the investment that made a 9% loss. But
L + P = 21000; therefore, 21000 – P = L
(loss = .09L = .09(21000 – P))
Since there was a net loss of 196, the loss will be > profit, and
.09(21000 – P) – .13P = 196
1890 – .09P – .13P = 196
1694 = .22P
P = 1694/.22 = 7700 invested for 13% profit ($1001)
L = 21000-7700 = 13300 invested at 9% loss ($1197)
1197 – 1001 = 196 net loss check!
7700 invested for profit
13300 invested at loss
This is a system of equations…
To solve this we make 2 equations.
Then we use substitution to solve one equation with the other…
Let x be the first investment and y be the second investment.
So if we total the investments we get
x + y = 2100
Investment 1, 13 % Profit = + 0.13 x
Investment 2, 09 % Loss = – 0.09 y
Her net loss was $196.00 is the value when we add the profit and the loss…
0.13 x – 0.9 y = – 196.00
Now we have 2 equations
1) x + y = 2100
2) 0.13 x – 0.9 y = – 196.00
Solve for 1 variable in terms of the other
y = 21000 – x
Substitute that equation into Equation 2
0.13 x – 0.09 (21000 – x) = -196.00
Distribute
0.13 x – 1890 + 0.09 x = -196.00
Get y b itself…
0.13 x + 0.09 x = -196.00 + 1890
0.22 x = 1694.00
Divide both sides
x = 7700
Now use that x to get y
y = 21000 – x
y = 21000 – 7700
y = 13300
So our two investments are 7700, and 13300