Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Activity

The tax on the sale of a car in Michigan is 6%. At a dealership in Ann Arbor, a car purchase also involves $120 in miscellaneous charges.

There are several quantities in this situation: the original car price, sales tax, miscellaneous charges, and total price.

For questions 1 - 4, write an equation to describe the relationship between all the quantities when given specific information.

1.

The original car price is $9,500.

Compare your answer:

$𝑇 = 9, 500 + 0.06 (9, 500) + 120$ , or $𝑇 = 1.06 (9, 500) + 120$

2.

The original car price is $14,699.

Compare your answer:

$𝑇 = 14, 699 + 0.06 (14, 699) + 120$ , or $𝑇 = 1.06 (14, 699) + 120$

3.

The total price is $22,480.

Compare your answer:

$22, 480 = 𝑝 + 0.06 𝑝 + 120$ , or $22, 480 = 1.06 𝑝 + 120$

4.

The original price is $p$ .

Compare your answer:

$𝑇 = 𝑝 + 0.06 𝑝 + 120$ , or $𝑇 = 1.06 𝑝 + 120$

5.

How would each equation you wrote change if the tax on car sales is $r$ % and the miscellaneous charges are $m$ dollars?

Compare your answer:

$𝑇 = 9, 500 + \frac{r}{100} (9, 500) + m$
$𝑇 = 14, 699 + \frac{r}{100} (14, 699) + m$
$22, 480 = p + \frac{r}{100} (p) + m$
$T = p + \frac{r}{100} (p) + m$

Equations equivalent to these are also correct.

Self Check

Sweet’s Candy Store charges $5.00 to fill a bag of candy. There is also a sales tax of 7% per purchase. Mrs. Smith buys 4 bags of candy for her children for Christmas. What is an equation that can represent the cost of the candy that Mrs. Smith buys?

$C=0.07+4(5)$
$C=4(5)$
$C=0.07(4(5))$
$C=0.07(4(5))+4(5)$

Additional Resources

Writing an Equation to Represent a Real-World Problem with Percentages

The steps for writing an equation to represent a real-world scenario with percentages are the same as before. Just be sure to change the given percent to a decimal before you use it in the equation.

Writing an Equation

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.

For example, what is an equation that can represent this scenario?

The label on Audrey’s yogurt said that one serving provided 12 grams of protein, which is 24% of the recommended daily amount. What is the total recommended daily amount of protein?

Here’s how to use the steps:

Step 1 - Read the problem.

The label on Audrey's yogurt said that one serving provided 12 grams of protein, which is 24% of the recommended daily amount. What is the total recommended daily amount of protein?

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

1 serving = 12 grams of protein
1 serving is 24% of recommended daily amount
Let $a$ = total amount of protein (in grams).

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

12 grams is 24% of the total amount

Step 4 - Translate the sentence into an equation.

$12 = 0.24 a$

Try it

Try It: Writing an Equation to Represent a Real-World Problem with Percentages

Analyze the situation and then write an equation that can represent the scenario.

One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?

1.

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

Compare your answer: 1 serving = 7 grams of fiber. 1 serving is 28% of the recommended daily amount.

2.

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

Compare your answer: $a$ = total amount of fiber (in grams)

3.

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

Compare your answer: 7 grams is 28% of the total amount

4.

What equation can be used to represent the scenario?

Compare your answer: $7 = 0.28 a$

1.2.4 Writing Equations to Represent Relationships with Percentages

Activity

Additional Resources

Writing an Equation to Represent a Real-World Problem with Percentages

Try It: Writing an Equation to Represent a Real-World Problem with Percentages