interest equations (X,y,z)

Question

Maricopa's Success scholarship fund receives a gift of $ 155,000. The money is invested in stocks, bonds, and CDs. CDs pay 3.5% interest, bonds pay 5% interest, and stocks pay 11.8% interest. Maricopa Success invests $50,000 more in bonds than in CDs. If the annual income from the investments is $9,605 , how much was invested in each account?

Answer 1

There is a few ways to do this. I personally set up two equations and solve by using elimination and substitution.

Let A represent stocks, Let B represent Bonds, and let C represent CDs.

Then A + B + C = 155,000

But we can substitute B in the equation and rewrite it as

A + C + (C + 50,000) = 155,000 or

A + 2C = 105,000

Similarly, we know that

.118A + .035C + .05(C+50,000) = 9,605

.118A + .035C + .05C + 2,500 = 9,605

.118A + .085C = 7,105

Now we have our two equations. We want to eliminate one of the variables by manipulating one of the equations and adding them together.

.118A + .085C = 7,105

A + 2C = 105,000

If I multiply the second equation by (-.118), I can eliminate the variable A.

(A + 2C = 105,000) X(-.118) =

-.118A - .236C = -12,390

Now we can add them together.

-.118A - .236C = -12,390

+ .118A + .085C = 7,105

- .151C = -5,285

C = -5,285 / -.151 = 35,000 (Amount invested in CDs)

We know there is $50,000 more invested in bonds than in CDs. So the amount invested in bonds is $85,000. The remaining $35,000 is invested in stocks.

Answer 2

x invest in CDs, (x + 50000) invest in bonds, and in stocks 155000 - x - (x + 50000) = 105000 - 2x.

So we have equation: 0.035x + 0.05(x + 50000) + 0.118(105000 - 2x) = 9605;

0.035x + 0.05x - 0.236x = 9605 - 0.05·50000 - 0.118·105000, - 0.151x = - 5285; from here x = - 5285/(- 0.151) = 35000;

Answer: invest in CD s x = $35000; invest in bond's, invest in bonds 35000 + 50000 = $85000,

invested in stocks 105000 - 2·35000 = $35000

Answer 3

.035cd+.05b+.118st

.035cd+((50,000+cd).05)+.118st=$164,605

With this imfo; this is the best I can do because there can be different combinations.