Chapter 8 - XYZ Custom Plus

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530<strong>Chapter</strong> 8 Linear Equations and Inequalities10. In a third granola bar, 28% ofthe calories are from fat. If oneserving of this bar contains 150calories, how many of thosecalories are from fat?Example 10The American Dietetic Association (ADA) recommendseating foods in which the calories from fat are less than 30% of the total calories.The nutrition labels from two kinds of granola bars are shown in Figure 1. Foreach bar, what percent of the total calories come from fat?Solution The information needed to solve this problem is located toward thetop of each label. Each serving of Bar I contains 210 calories, of which 70 caloriescome from fat. To find the percent of total calories that come from fat, we mustanswer this question:70 is what percent of 210?Nutrition FactsServing Size 2 bars (47g)Servings Per Container 6Amount Per ServingCalories 210Calories from Fat 70% Daily Value*Total Fat 8g 12%Saturated Fat 1g 5%Cholesterol 0mg 0%Sodium 150mg 6%Total Carbohydrate 32g 11%Dietary Fiber 2g 10%Sugars 12gProtein 4g* Percent Daily Values are based on a 2,000 caloriediet. Your daily values may be higher or lower dependingon your calorie needs.Nutrition FactsServing Size 1 bar (21g)Servings Per Container 8Amount Per ServingCalories 80Calories from Fat 15% Daily Value*Total Fat 1.5g 2%Saturated Fat 0g 0%Cholesterol 0mg 0%Sodium 60mg 3%Total Carbohydrate 16g 5%Dietary Fiber 1g 4%Sugars 5gProtein 2g* Percent Daily Values are based on a 2,000 caloriediet. Your daily values may be higher or lower dependingon your calorie needs.Figure 1For Bar II, one serving contains 80 calories, of which 15 calories come fromfat. To find the percent of total calories that come from fat, we must answer thisquestion:15 is what percent of 80?Translating each equation into symbols, we have70 is what percent of 210 15 is what percent of 8070 = x ⋅ 210 15 = x ⋅ 80x = _70210 x = 15 _80 x = 0.33 to the nearest hundredth x = 0.19 to the nearest hundredthx = 33% x = 19%Comparing the two bars, 33% of the calories in Bar I are fat calories, whereas19% of the calories in Bar II are fat calories. According to the ADA, Bar II is thehealthier choice.Answer10. 42 caloriesGetting Ready for ClassAfter reading through the preceding section, respond in your ownwords and in complete sentences.1. What is a formula?2. How do you solve a formula for one of its variables?3. What are complementary angles?4. What does percent mean?
8.5 Problem Set531Problem Set 8.5A Use the formula P = 2l + 2w to find the length l of a rectangular lot if [Examples 1–2]1. The width w is 50 feet and the perimeter P is 300 feet100 feet2. The width w is 75 feet and the perimeter P is 300 feet75 feet3. For the equation 2x + 3y = 6a. Find y when x is 0. 2b. Find x when y is 1. _3 2 c. Find y when x is 3. 04. For the equation 2x − 5y = 20a. Find y when x is 0. −4b. Find x when y is 0. 10c. Find x when y is 2. 15_5. For the equation y = − 1 3 x + 2a. Find y when x is 0. 2b. Find x when y is 3. −3c. Find y when x is 3. 1_6. For the equation y = − 2 3 x + 1a. Find y when x is 0. 1b. Find x when y is −1. 3c. Find y when x is −3. 3AUse the formula 2x + 3y = 6 to find y if7. x is 308. x is −29. x is 0_ 103 210. x is −34AUse the formula 2x − 5y = 20 to find x if11. y is 212. y is −413. y is 014. y is −615010−5AUse the equation y = (x + 1) 2 − 3 to find the value of y when15. x = −216. x = −117. x = 118. x = 2−2−316
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