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percentage and interest

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by BTGmoderatorRO » Sun Oct 08, 2017 11:20 am
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5
OA is a.

I'm confused on how to set up the formulas here. Can any experts help?
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by [email protected] » Sun Oct 08, 2017 11:35 am
Hi Roland2rule,

We're told that John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. In addition, John neither made a profit nor a loss. We're asked what fraction of his savings was invested in investment X. You can approach this question in a couple of different ways; here's how you can solve it Algebraically:

X = total gained 10%
(1-X) = total that lost 15%

Since John's gains were cancelled out by his losses, we need to define the gain and loss and set them equal to one another:

Gain = (.1)(X) = .1X gain
Loss = (.15(1-X) = .15 - .15X loss

.1X = .15 - .15X
.25X = .15
25X = 15
X = 15/25 = 60%

Thus, 60% of John's savings was put into investment X.

Final Answer: A

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Re: percentage and interest

by Scott@TargetTestPrep » Sat Jan 18, 2020 1:05 pm
BTGmoderatorRO wrote: ↑
Sun Oct 08, 2017 11:20 am
 John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5
OA is a.

I'm confused on how to set up the formulas here. Can any experts help?
Solution:

We can let the amount in investment X be 100, so it earns a profit of 0.1 x 100 = 10. Now let y = the amount in investment Y and, since it lost 15%, we can create the equation:

0.15y = 10

y = 10/0.15 = 1000/15 = 200/3

Therefore, the total amount of the two investments is 100 + 200/3 = 500/3, and investment X is:

100/(500/3) = 100 x 3/500 = 3/5 of the total investment.

Alternate Solution:

Let A be John’s total savings and k be the fraction of savings invested in investment X; i.e. Ak is the amount invested in X and A(1 - k) is the amount invested in Y.

Since John made neither a profit nor a loss, the profit from investment X must equal the loss from investment Y; i.e.

(0.1)Ak = (0.15)A(1 - k)

0.1k = 0.15(1 - k)

10k = 15(1 - k)

10k = 15 - 15k

25k = 15

k = 15/25 = 3/5

Answer: A

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