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Algebra 1

1.2.3 Writing Equations to Represent Relationships

Algebra 11.2.3 Writing Equations to Represent Relationships

1.2.3 Writing Equations to Represent Relationships

1.2.3 • Writing Equations to Represent Relationships

Activity

Write an equation to represent each situation.

1.

Blueberries are $4.99 a pound. Diego buys bb pounds of blueberries and pays $14.95.

2.

Blueberries are $4.99 a pound. Jada buys pp pounds of blueberries and pays cc dollars.

3.

Blueberries are dd dollars a pound. Lin buys qq pounds of blueberries and pays tt dollars.

4.

Noah earned nn dollars over the summer. Mai earned $275, which is $45 more than Noah did.

5.

Noah earned vv dollars over the summer. Mai earned mm dollars, which is 45 dollars more than Noah did.

6.

Noah earned ww dollars over the summer. Mai earned xx dollars, which is yy dollars more than Noah did.

7.

How are the equations you wrote for the blueberry purchases like the equations you wrote for Mai’s and Noah’s summer earnings? How are they different?

Self Check

Max and Jules are renting a car for their 3-day trip. The rental company charges $50 per day and $0.40 per mile driven. Which is a possible equation for their cost of the rental car?
  1. C = 50 ( 3 ) + 0.40 m
  2. C = 50 ( 3 ) + 40 ( 3 ) + 0.40 m
  3. C = 50 m + 40 ( 3 )
  4. C = 50 ( 3 ) + 40 m

Additional Resources

Writing an Equation to Represent a Real-World Problems

Here are the steps to writing an equation to represent a real-world scenario:

Step 1 - Read the problem.

Step 2 - Identify the variables and known values. If needed, sketch a picture of the scenario.

Step 3 - Write a sentence using the relationship among the values.

Step 4 - Translate the sentence into an equation.

Example

Write the following statement algebraically using symbols: Peanuts cost $3.59 per pound. Max buys pp pounds of peanuts and pays $10.77.

Step 1 - Read the problem.

Peanuts cost $3.59 per pound. Max buys pp pounds of peanuts and pays $10.77.

Step 2 - Identify the variables and known values. If needed, sketch a picture of the scenario.

$3.59 = cost per pound of peanuts

$10.77 = total cost of peanuts bought

pp = number of pounds of peanuts bought

Step 3 - Write a sentence using the relationship among the values.

The cost per pound times the number of pounds bought equals the total cost of peanuts

Step 4 - Translate the sentence into an equation.

3.59(p)=10.773.59(p)=10.77

Try it

Writing an Equation to Represent a Real-World Problem

Translate the following scenario into an equation:

A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?

1.

After reading the problem, what are some of the known variables identified in the description?

2.

Identify a variable and describe what it represents for this scenario.

3.

What sentence can be used to describe the relationship among the values?

4.

What equation can be used to represent the scenario?

Video: Writing an Equation to Represent a Real-World Problem

Watch the following video to learn more about how to write an equation to represent a real-world problem.

Writing an Equation to Represent a Real-World Problem

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