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Algebra 1 - Linear Modeling Homework Solutions - Prof. Violeta Kovacev-Nikolic, Assignments of Algebra

Western Michigan University (WMU)Algebra

Prof. Violeta Kovacev-Nikolic

Solutions to various problems related to linear modeling in algebra 1, including finding expressions and intercepts of linear functions, determining costs for different services, and understanding the relationship between hours and charges.

Typology: Assignments

Pre 2010

Uploaded on 07/28/2009

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MATH 1100 - Algebra 1 Linear Modeling

- 1 -

HW_5a

#10./p.44 (Suppl.) A linear function

(

)

y h x

satisfies

(

)

1 3

and

(

)

1 5

− =

a. Find the expression of

(

)

h x

b. Find the values of

(

)

−

and

(

)

c. Find the value of

such that

(

)

h x

= −

#13. (Online Suppl.) If

(

)

y f x

is a linear function such that

(

)

1 21

− = −

and

(

)

5 3

, then what is the value of

(

)

Discover Assignments of Algebra Western Michigan University (WMU)

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HW_5a

#10./p.44 (Suppl.) A linear function y = h x( ) satisfies h ( 1 ) = 3 and f ( − 1 ) = 5.

a. Find the expression of h x( ).

b. Find the values of h ( − 3 )and h ( 4 ).

c. Find the value of x such that h x( ) = − 5.

#13. (Online Suppl.) If y = f ( x) is a linear function such that f ( − 1 ) = − 21 and f ( 5 ) = 3 , then what is the value of

f ( 1 )?

#10./p.44 (Suppl.) A linear function y = h x( )satisfies h ( 2 ) = 9 and h ( 4 ) = 13. Find the intercepts of the graph of the

function.

#40./p.47 (Suppl.) A printer charges a fixed rate for each book she prints, plus a charge for typesetting that is independent of the number of books printed. If she charges $740 for printing 100 books and $1300 for printing 180 books, then: a. Express the cost as a function of the number of books printed. b. What is the typesetting charge? c. What does the slope of the line represent? d. What would be the cost of printing 250 books?

#5. (Extra) Joe charges $8.00 per hour for mowing lawns, plus $2.50 per job to cover equipment maintenance.

a. Write an equation for Joe’s charges C t( )with respect to the number t of hours that it takes to complete the job.

b. Use the previous formula to find the total cost to complete a 3.5 hours job. c. If he charges a total of $28.50 for a particular job, how much time did it take Joe to complete the job?

#16./p.45 (Suppl.) A company makes T-shirts which it sells for $20 each. The total cost (material and labor) to make a single shirt is $16, plus the company has a yearly overhead (utilities, taxes, etc.) cost of $8 500.

a. Express the total cost C ( x )to make x T-shirts in a year as a linear function of x. Note that C ( 0 )=$8500.

b. What is the total cost of making 1000 T-shirts? How many shirts does the company have to sell to “break even?” Note: profit = (revenue, i.e. total income from sales) - (total costs). (“break even” = no profit )