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## Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay

Question

Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay 4.5% interest, and stocks pay 10.4% interest. Country days invests $70000 more in bonds than CDs. If the annual income from the investments is $8555, how much was invested in stocks, bonds, and CDs?

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2021-09-13T15:43:38+00:00
2021-09-13T15:43:38+00:00 1 Answer
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## Answers ( )

Answer:Step-by-step explanation:Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

0.0275c +.045b +0.104s = 8555 . . . . . total income earned

-c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

.0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

.0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

s = 65000 -2c . . . . . . . expression we can substitute for s

0.0725c +0.104(65000 -2c) = 5405

-0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

c = 1355/.1355 = 10,000

s = 65000 -2×10000 = 45,000

b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively._____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is …