Activity In this activity, you will identify proportional relationships found in tables.

Tim wants to buy several pairs of jeans. He compares the prices at a store in his neighborhood and at an online store. He finds that a pair of jeans costs $24 at the local store. If he buys online, each pair would cost $22, and he would have to pay a shipping fee of $6 per order.

Part A
Complete the tables to relate the number of pairs of jeans to the cost of the jeans at each store. Assume that Tim is placing a single order, and ignore any taxes.

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Local Store Online Store
Pairs of Jeans Cost Pairs of Jeans Cost
1 $24 1 $28
2 $48 2 $50
3 $72 3 $72
At the local store, the cost of 1 pair of jeans is $24 and the cost of 3 pairs is $24 × 3 = $72. At the online store, the cost of 2 pairs of jeans is ($22 × 2) + $6 = $50 and the cost of 3 pairs is ($22 × 3) + $6 = $72.

Part B
Look at the table that represents the local store. For each row in the table, find the ratio of the number of pairs of jeans to the cost of the jeans.

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In the first row, the ratio is .
In the second row, the ratio is , which simplifies to .
In the third row, the ratio is , which simplifies to .

Part C
Are the ratios that you calculated in part B equivalent? Based on these ratios, what can you conclude about the relationship between the number of pairs of jeans that Tim buys at the local store and the cost?

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The three ratios are equivalent. This means the relationship between the number of pairs of jeans and their cost at the local store is a proportional relationship.

Part D
Next, look at the table that represents the online store. For each row in the table, find the ratio of the number of pairs of jeans to the cost of the jeans.

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In the first row, the ratio is .
In the second row, the ratio is ,which simplifies to .
In the third row, the ratio is ,which simplifies to .

Part E
Are the ratios that you calculated in part D equivalent? Based on these ratios, what can you conclude about the relationship between the number of pairs of jeans that Tim buys at the online store and the cost?

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Part F
The local store where Tim shops charges a 7% sales tax for clothing. Complete the table by figuring the cost of the jeans after sales tax is applied. The first row has been done for you.

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Part G
From part F, find the ratio of the number of pairs of jeans to the cost with sales tax for each row in the table.

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Part H
Are the ratios that you calculated in part G equivalent? Show your work to support your answer. What does this tell you about the relationship between the number of pairs of jeans and the cost with sales tax applied?

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Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

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