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Algebra 1

1.1.2 Creating Expressions to Estimate Cost, Part 1

Algebra 11.1.2 Creating Expressions to Estimate Cost, Part 1
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Activity

Imagine your class is having a pizza party.

Work with your group to plan what to order and to estimate what the party would cost.

Supreme pizza.
1.

What is your favorite type of pizza to order?

2.

How many toppings are on your favorite type of pizza?

3.

What type of crust does your favorite pizza have?

For 4 - 9, use the following group instructions.

Work with a group to research the cost of ordering pizza from a local restaurant. Then, determine what to order for the class pizza party and determine how much it would cost. Answer the following questions regarding your group's plan.
4.

What is the cost estimate for your group's planned class party?

5.

Write down one expression that show how your group’s cost estimate was calculated.

6.

In your expression, which quantities, if any, might change on the day of the party?

7.

Rewrite your expression, replacing the quantities that might change with letters.

8.

What do the letters represent?

9.

How would you convince the class to go with your group’s plan?

Are you ready for more?

Extending Your Thinking

A local pizzeria sells gourmet pizzas for the prices posted below. Remember the sizes are determined by the diameter of each pizza. Compare the cost per square inch of the sizes.

Pizza size 10” Small 12” Medium 14” Large 16” XLarge
Price $12.99 $15.99 $19.99 $21.99
1.

How did you determine the cost per square inch of each pizza?

2.

Which size pizza is the better deal?

3.

Which size pizza is the most expensive per square inch?

4.

What is the difference in price per square inch between the most and least expensive sizes?

Self Check

A ninth-grade class is ordering pizza for lunch. There are  n students in the class. Each slice of pizza costs $3 and the delivery fee is $8. Which expression represents the total cost if each student gets 2 slices of pizza?
  1. 3 n + 8
  2. ( 2 ) 3 n + 8
  3. ( 2 ) 3 n
  4. 3 n

Additional Resources

Translate an English Phrase to an Algebraic Expression

You can use the following operation symbols to translate English phrases into algebraic expressions.

Look closely at these phrases using the four operations:

the sum of aa and bb

the difference of aa and bb

the product of aa and bb

the quotient of aa and bb

Then, identify other phrases that represent the same algebraic concepts.

Each phrase tells us to operate on two numbers. Look for the words "of" and "and" to find the numbers.

Later in this course, we’ll apply our skills in algebra to solving applications. The first step will be to translate an English phrase to an algebraic expression.

Example

The length of a rectangle is 14 less than the width. Let ww represent the width of the rectangle. Write an expression for the length of the rectangle.

Step 1 - Write a phrase about the length of the rectangle.

14 less than the width

Step 2 - Substitute ww for "the width."

14 less than ww

Step 3 - Rewrite less than as subtracted from.

14 subtracted from ww

Step 4 - Translate the phrase into algebra.

w−14w−14

Try it

Try It: Translate an English Phrase to an Algebraic Expression

Translate the following into an algebraic expression:

June has dimes and quarters in her purse. The number of dimes is seven less than four times the number of quarters. Let qq represent the number of quarters. Write an expression for the number of dimes.

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