*label*Mathematics

### Question Description

Week Three - Application Assignment

Answer the following questions in a Word document and upload the document to the appropriate drop box.

1) A museum borrows $2,000,000 at simple annual interest to purchase new

exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. You do not have to solve the system.

2) At a local store, the numbers of gallons of skim milk, 2% milk, and whole milk sold over the weekend are represented by a matrix A.

Skim 2% Whole

Friday 40 64 52

Saturday 60 82 76

Sunday 76 96 84

The selling prices per gallon and the profits per gallon for the three types of milk are represented by B.

Selling price Profit

Skim $3.45 $1.20

2% $3.65 $1.30

Whole $3.85 $1.45

a) Compute AB and interpret the result.

b) Find the store’s total profit from milk sales for the weekend

3) A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. A customer plans on spending $300 on 10 centerpieces with each centerpiece containing 12 flowers, with twice as many roses as the number of irises and lilies combined.

a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.

b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

4) One hundred liters of a 50% solution of a chemical mixture is obtained by mixing a 60% solution with a 20% solution. Using a system of linear equations determine how many liters of each solution are required to obtain the 50% mixture. Solve the system using matrices.

## Tutor Answer

Attached.

Running Head: MATHEMATICS

1

Mathematics:

Name:

Institution:

Date:

MATHEMATICS

2

Question One

The linear equations to solve the amount borrowed at the specific interest rate

Solution

Simple interest on the amount borrowed at 7%

I=

7

×x×T

100

Simple interest on the amount borrowed at 7%

I=

8.5

×y×T

100

Simple interest on the amount borrowed at 7%

I=

𝑇𝑜𝑡𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 =

9.5

×z×T

100

9.5

8.5

7

×𝑧×𝑇+

×𝑦×𝑇+

× 𝑥 × 𝑇 = 169,750

100

100

100

Since the $169,750 interest given is annual then T=1

The equation simplifies to

0.095𝑧 + 0.085𝑦 + 0.07𝑥 = 169,750

The equation simplifies to:

19z + 17y + 14x = 33,950,000 … … … … … . . equation 1

The amount borrowed= $ 2,000,000 and therefore:

x + y + z = 2,000,000 … … … … … … equation 2

Since the amount borrowed at 8.5% is four times the amount borrowed at 9.5% then:

y = 4z … … … … … … … … … … ...

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