Question

County day scholarship fund receives a gift of $130,000 the money is invested in stocks, bonds and CDs. CDs pay 2% interest, bonds pay 2.9% interest, and stocks pay 9.9% interest. country day invests $25000 more in bonds than in CDs. if the annual income from the investment is $8885, how much was invested in each vehicle?
country day invested $______ in stocks.
country day invested $______ in bonds.
country day invested $______ in CDs.
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Answer 1

Answer:

$15,000 was invested in CDs.

$40,000 was invested in bonds.

$75,000 was invested in stocks.

Step-by-step explanation:

Let C be the amount invested for CDs, B be the amount invested for bonds, and S be the amount invested for stocks.

We know that the total amount invested must be $130,000 because that was the amount given to the Scholarship Fund. So:

$C+B+S=130000$

We know that CDs pay 2% or 0.02 interest; Bonds pay 2.9% or 0.029 interest; and Stocks pay 9.9% or 0.099 interest. In total, the investment earned $8,885. So:

$0.02C+0.029B+0.099S=8885$

Let's remove the decimals by multiplying everything by 1000. This yields:

$20C+29B+99S=8885000$

Now, we know that $25000 more was invested in bonds than CDs. So:

$B=25000+C$

We have a triple system of equations. We can solve this using substitution. Let's substitute our third equation into the second equation. This yields:

$20C+29(25000+C)+99S=8885000$

We want to isolate the C variable. Here, we removed the B but we still have an S.

So, to remove the S, we can go back to our first equation. We have:

$C+B+S=13000$

Subtract C and B from both sides:

$S=130000-C-B$

We can now substitute this for S:

$20C+29(25000+C)+99(130000-C-B)=8885000$

We got a B again. But, we already know what B is. Substitute:

$20C+29(25000+C)+99(130000-C-((25000)+C))=8885000$

So, our equation is now in terms of C. Solve for C. Distribute on the far right:

$20C+29(25000+C)+99(130000-C-25000-C)=8885000$

Combine like terms:

$20C+29(25000+C)+99(105000-2C)=8885000$

Distributive Property:

$20C+725000+29C+10395000-198C=8885000$

Combine like terms:

$(20C+29C-198C)+(725000+10395000)=8885000$

Add:

$-149C+11120000=8885000$

Subtract 1112000 from both sides:

$-149C=-2235000$

Divide both sides by -149:

$C=15000$

So, a total of $15,000 was invested in CDs.

Since $25,000 more was invested in bonds than in CDs, this means that a total of $25000+$15000 or $40,000 was invested in bonds.

To find out how much was invested in stocks, we can use our first equation again:

$C+B+S=130000$

Substitute 15000 for C and 40000 for B:

$15000+40000+S=130000$

Add:

$55000+S=130000$

Subtract 55000 from both sides:

$S=\ 75000$

So, $15,000 was invested in CDs, $40,000 was invested in bonds, and $75,000 was invested in stocks.

And we're done!

Answer 2

Answer:

$15,000 was invested in CDs.

$40,000 was invested in bonds.

$75,000 was invested in stocks.

Step-by-step explanation: