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:
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:
Let's remove the decimals by multiplying everything by 1000. This yields:
Now, we know that $25000 more was invested in bonds than CDs. So:
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:
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:
Subtract C and B from both sides:
We can now substitute this for S:
We got a B again. But, we already know what B is. Substitute:
So, our equation is now in terms of C. Solve for C. Distribute on the far right:
Combine like terms:
Distributive Property:
Combine like terms:
Add:
Subtract 1112000 from both sides:
Divide both sides by -149:
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:
Substitute 15000 for C and 40000 for B:
Add:
Subtract 55000 from both sides:
So, $15,000 was invested in CDs, $40,000 was invested in bonds, and $75,000 was invested in stocks.
And we're done!