BIG: idea Variable

You can use variables to represent quantities that are unknown or vary and to write expressions and equations.

Task 1

Solve. Show all of your work and explain your steps.

A riding-stable manager is planning a nutritional diet for 6 horses. The manager finds the table below in a guide about horse health. The cost of 1000 Calories of horse feed is $.15. What is the cost per day to feed the 6 horses? (Hint: First, try writing an expression for the number of daily Calories needed for h horses.)

Task 2

Use the table below to complete each part.

1. Copy the table. Extend the table by writing expressions for y when x = 5, 6, and 7.
2. Simplify each expression for y in your table from part (a). What pattern do you notice in the simplified expressions?
3. Write an equation that relates x and y. Use your equation to find the value of y when x = 15.

BIG: idea Properties

The properties of real numbers describe relationships that are always true. The properties of real numbers are true in both arithmetic and algebra. You can use them to rewrite expressions.

Task 3

Solve. Show all of your work and explain your steps.

You are buying gifts for 10 people. You decide to buy each person either a CD or a DVD. A CD costs $12 and a DVD costs $20.

1. Let c = the number of CDs you decide to buy. What is an expression in terms of c for the number of DVDs you buy?
2. What is an expression in terms of c for the cost of the CDs? For the cost of the DVDs?
3. Write and simplify an expression in terms of c for the total cost of all the gifts you buy. What properties of real numbers did you use to simplify the expression?