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On two investments totaling$8,000, Lydia lost4 % on one and earned6% on the other. If her net annual receipts were$400, how much was each investment?

User Evan Stoddard
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1 Answer

16 votes
16 votes

Let's say,

The investment1 = x

investment2 = y

As given, two investments totaling to 8000$. Therefore,

x + y = 8000. (i)

The net loss on investment x (4%) = - 4% of x = - 4/100 * x = - 0.04x

The net profit on investment y (6%) = 6% of x = 6/100 * x = 0.06x

As given, the net receipt is = 400$

Therefore,

-0.04x + 0.06y = 400. (ii)

Now, solve both equations simultaneously.

from eq (1), x = 8000 - y. Put this in eq(ii).

-0.04(8000 - y) + 0.06y = 400

-320 + 0.04y + 0.06y = 400

0.1y = 400 + 320

0.1y = 720

Multiply both sides by (10), we get

10* (0.1y) = 10 * 720

y = 7200

Now, put the value of y in eq (i) and get the value of x

x + y = 8000

x + 7200 = 8000

x = 800

Hence, the first investment is 800, while the second is 7200.

User Pflz
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