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Pat invested a total of $3,000. Part of the money was invest

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Pat invested a total of $3,000. Part of the money was invest [#permalink] New post 24 May 2019, 01:52
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Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent?


[Reveal] Spoiler: OA
$800 at 10% and $2,200 at 8%


Math Review
Question: 13
Page: 244
Difficulty: medium/hard

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Re: Pat invested a total of $3,000. Part of the money was invest [#permalink] New post 25 May 2019, 04:08
Expert's post
Carcass wrote:
Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent?


[Reveal] Spoiler: OA
$800 at 10% and $2,200 at 8%


Math Review
Question: 13
Page: 244
Difficulty: medium/hard


Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest.
Let x = the amount of money invested at 8%
So, 3000-x = the amount of money invested at 10%

If the interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent?
1 year interest on 8% account = 0.08x
1 year interest on 10% account = 0.1(3000 - x)

We can write: 0.08x + 0.1(3000 - x) = 256
Expand: 0.08x + 300 - 0.1x = 256
Simplify: 300 - 0.02x = 256
Subtract 300 from both sides to get: -0.02x = -44
Solve: x = -44/-0.02 = 44/0.02 = 4400/2 = 2200

So, $2200 was invested at 8%, and $800 was invested at 10%

Cheers,
Brent
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Re: Pat invested a total of $3,000. Part of the money was invest   [#permalink] 25 May 2019, 04:08
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Pat invested a total of $3,000. Part of the money was invest

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