a)What expression represents the total cost of the job?b)What is the cost for a job requiring 2 h?c)The company charges half as much for a second technician. Write an expression showing the total cost if two technicians install a new furnace. Simplify your expression by combining like terms.20.A publisher makes books for a number of distributors. For one book, the charge to the distributor is represented by a fixed cost of $3000 plus $16 per book.a)Write an expression for the cost that a distributor is charged for bcopies of this book.b)How much do 600 books cost?c)What is the cost per book if 600 are ordered?d)What is the cost per book if 1000 are ordered?188MHR •Chapter 5
21.Raj was told to write an expression equivalent to 3x-8 -5x+9.3x - 8 - 5x + 9 = 3x - 5x - 8 + 9= 2x - 1a)What errors did he make?b)Show the correct response.22.The diagram represents a piece of string.3x+ 72x- 5xa)What is an expression for the total length of the string?b)Combine like terms to get the simplest expression possible for the length of the string.Extend23.When would the expressions x+y+3 and x+w+3 be equal? How do you know?24.A department store marks up wholesale prices 40% to get its retail or selling price.a)Complete the following table. The first row has been done for you. Wholesale Price ($)Expression For Retail PriceRetail Price ($)8.008 +(0.4)(8)11.2012.0030.00xb)How could you find the retail price if the wholesale price is x+10 dollars? Show two ways to find the answer.25.Zip Publishers will print posters for fundraising events for an initial cost of $100 plus $2 per poster. Henry’s Printers charges $150 plus $1 per poster.a)Write an expression for each company, showing the total cost for any number of posters.b)What is the cost of 125 posters from each company?c)What is the total cost if you print 200 posters at each company? Show two different ways to find the answer.Refer to the Math Link for section 5.1 on page 182. Represent each item with a variable:a =blender b =watch c =bookd =soccer ball e=drum f =coffeemakera)Rewrite all your combinations that add to $100, using the letters ato f. Arrange each combination in alphabetical order. For example, a+e +d+3cwould be written as a +3c+d+e.b) The example in part a) can be used to find other combinations. Notice that ehas a value of $40. What other items from the list have a value of $40? By substituting into e the letter or letters that combine to a total value of $40, you arrive at another answer. Do not forget to combine like terms and arrange each expression in alphabetical order. What other combinations can you find using substitution?c) If you were asked to find combinations of the items that add to $101, how could you use algebra to help you? Give two ways that algebra could help you.5.2 Equivalent Expressions •MHR189
5.3Focus on…After this lesson, you will be able to…• add polynomial expressions• subtract polynomial expressions• solve problems using the addition and subtraction of polynomialsAdding and Subtracting PolynomialsA music store rents out a drum kit for $55 per month, plus
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