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EXAMPLE 4

EXAMPLE 4 Solve a multi-step problem SHOPPING A discount shoe store is having a sale, as described in the advertisement shown. • Use the information in the ad to write a system of inequalities for the regular footwear prices and possible sale prices.

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EXAMPLE 4

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  1. EXAMPLE 4 Solve a multi-step problem SHOPPING A discount shoe store is having a sale, as described in the advertisement shown. • Use the information in the ad to write a system of inequalities for the regular footwear prices and possible sale prices. • Graph the system of inequalities. • Use the graph to estimate the range of possible sale prices for footwear that is regularly priced at $70.

  2. STEP 1 Write a system of inequalities. Let xbe the regular footwear price and let ybe the sale price. From the information in the ad, you can write the following four inequalities. EXAMPLE 4 Solve a multi-step problem SOLUTION x ≥ 20 Regular price must be at least $20. x ≤ 80 Regular price can be at most $80. y ≥ 0.4x Sale price is at least (100 – 60)% = 40% of regular price. y ≤ 0.9x Sale price is at most (100 – 10)% = 90% of regular price.

  3. STEP 2 Graph each inequality in the system.Then identify the region that is common to all the graphs. It is the region that is shaded. Identify the range of possible sale prices for $70 footwear. From the graph you can see that when x = 70, the value of yis between these values: STEP 3 EXAMPLE 4 Solve a multi-step problem 0.4(70) = 28 and 0.9(70) = 63 So, the value ofysatisfies28 ≤ y ≤ 63.

  4. ANSWER Therefore, footwear regularly priced at $70 sells for between $28 and $63, inclusive, during the sale. EXAMPLE 4 Solve a multi-step problem

  5. 7. What if? In Example 4, suppose the advertisement showed a range of discounts of 20%–50% and a range of regular prices of $40–$100. b. Use the graph to estimate the range of possible sale prices for footwear that is regularly priced at $60. for Examples 4 GUIDED PRACTICE a. Write and graph a system of inequalities for the regular footwear prices and possible sale prices.

  6. STEP 1 Write a system of inequalities. Let xbe the regular footwear price and let ybe the sale price. From the information in the ad, you can write the following four inequalities. for Examples 4 GUIDED PRACTICE SOLUTION x ≥ 40 Regular price must be at least $40. x ≤ 100 Regular price can be at most $100. y ≥ 0.5x Sale price is at least (100 – 50)% = 50% of regular price. y ≤ 0.8x Sale price is at most (100 – 20)% = 80% of regular price.

  7. STEP 2 Graph each inequality in the system. Then identify the region that is common to all the graphs. It is the region that is shaded. for Examples 4 GUIDED PRACTICE

  8. ANSWER Therefore, footwear regularly priced at $60 sells for between $30 and $48. Identify the range of possible sale prices for $60 footwear. From the graph you can see that when x = 70, the value of yis between these values: STEP 3 for Examples 4 GUIDED PRACTICE 0.5(60) = 30 and 0.8(60) = 48 So, the value ofysatisfies30 ≤ y ≤ 48.

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