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Financial Algebra

Robert Gerver, Richard Sgroi

Chapter 8

Independent Living

Educators


Problem 1

Explain how this quote can be interpreted in light of what you have learned.

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Problem 2

Use the interval $25 \%-30 \%$ to find the monetary range that is recommended for the monthly housing budget in each situation. Round to the nearest dollar.
a. Mark makes $\$ 7,000$ per year.
b. Iinda makes $\$ 7,000$ per wonth.
c. Meghan makes $\$ 1,500$ per week.

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Problem 3

Jessica's financial advisor believes that she should spend no more than 28$\%$ of her gross monthly income for housing. She has determined that amount is $\$ 1,400$ per month. Based on this amount and her advisor's recommendation, what is Jessica's annual salary?

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Problem 4

Abe makes $\$ 18.50$ per hour. He works 37 hours a week. He pays 23$\%$ of his gross earnings in federal and state taxes and saves 5$\%$ of his monthly gross income. He is considering renting an apartment that will cost $\$ 1,500$ per month.
a. Is this monthly rental fee within the recommended $25 \%-30 \%$ housing expense range?
b. Based upon his expenses, can he make the monthly payments?

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Problem 5

Rachel is considering moving into a one-bedroom apartment in Glen Gardens. The apartment has a monthly rent of $\$ 1,300 .$ Here are the fees that she has been quoted. How much is she expected to pay up front in order to rent this apartment?

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Problem 6

Milena has a gross biweekly income of $\$ 2,200 .$ She pays 18$\%$ in federal and state taxes, puts aside 10$\%$ of her income to pay off her school loan, and puts 5$\%$ of her income aside for savings. She is considering an apartment that rents for $\$ 1,200$ per month.
a. Is this monthly rental fee within the recommended $25 \%-30 \%$ housing expense range?
b. Based on her expenses, can she make the monthly payments?

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Problem 7

A moving helper company gave Mike these two quotes. Use a system of equations to determine the hourly rates for loading/unloading and packing/ unpacking.

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Problem 8

Jaden received these two estimates from a moving company. Write and solve a system of equations to determine the hourly loading/unloading fee and the mileage charge for the truck rental.

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Problem 9

Ann obtained this list of apartments.
a. Use linear regression analysis to determine if there is a correlation between the square footage and the monthly rent.
b. Determine the regression equation. Round the numbers in the equation to the nearest hundredth.
c. Use your regression equation to determine the price you might expect to pay for an 810-square foot apartment.

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Problem 10

Use the information from Exercise 9.
a. Determine the correlation coefficient and linear regression equation that expresses the square footage as a function of the monthly rent. Round the numbers in the equation to the nearest hundredth.
b. Use your regression equation to determine the square footage you might expect if renting a $\$ 1,710$ apartment.

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Problem 11

Dave wants to rent a two-bedroom apartment in City Fields. The apartment has a monthly rent of $D$
dollars. Here are the fees that he has been quoted. Write an algebraic expression that represents the
amount he is expected to pay before renting the apartment.

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Problem 12

The square footage and monthly rental of 10 similar one-bedroom apartments yield the linear regression $y=0.775 x+950.25,$ where $x$ represents the square footage of the apartment and $y$ represents the monthly rental price. Grace can afford $\$ 1,500$ per month rent. Using the equation, what size apartment should she expect to be able to rent for that price?

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Problem 13

The square footage and monthly rental of 10 similar two-bedroom apartments yield the linear regression formula $y=1.165 x+615.23$ where $x$ represents the square footage of the apartment and $y$ represents the monthly rental price.
a. Use the formula to determine the monthly rent for an apartment that has $1,500$ square feet.
b. Based upon the recommendation that you should spend no more than 28$\%$ of your monthly gross income on housing, can Jacob afford this rental if he makes $\$ 8,000$ each month. Explain.

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Problem 14

WeMoveU charges for moving according to the rate schedule shown. Nicky is moving a distance of
150 miles and needs 7 hours of loading/unloading and 5 hours of packing/unpacking. What will her
moving cost be if the service also charges 8$\%$ tax on the total?

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Problem 15

Van 4 Hire charges for moving according to this rate schedule. Nicky is moving a distance of $D$
miles and needs $A$ hours of loading/unloading and $B$ hours of packing/unpacking. Write an
algebraic expression that represents her total moving cost.

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