Solve Proportions Using Cross Products

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Solve Proportions Using Cross Products Warm Up Lesson Presentation Lesson Quiz

Warm-Up Solve the proportion. 1. = t 32 7 16 2. = 18 24 b 12 ANSWER 14 ANSWER 9 3. = 21 n 28 32 4. = 4 12 11 p ANSWER 24 ANSWER 33

Warm-Up 5. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? ANSWER 45 tomatillos

Example 1 Solve the proportion = . 8 x 6 15 = 8 x 6 15 8 15 = x 6 Write original proportion. 8 15 = x 6 Cross products property 120 = 6x Simplify. 20 = x Divide each side by 6. The solution is 20. Check by substituting 20 for x in the original proportion. ANSWER

Example 1 CHECK 8 20 6 15 = ? Substitute 20 for x. 8 15 = 20 6 ? Cross products property 120 = 120 Simplify. Solution checks.

What is the value of x in the proportion = ? 4 x 8 3 x – C 3 A – 6 B Example 2 What is the value of x in the proportion = ? 4 x 8 3 x – C 3 A – 6 B – 3 D 6 SOLUTION 4 x = 8 – 3 Write original proportion. 4(x – 3) = x 8 Cross products property 4x – 12 = 8x Simplify. –12 = 4x Subtract 4x from each side. –3 = x Divide each side by 4. The value of x is –3. The correct answer is B. ANSWER A B C D

Guided Practice Solve the proportion. Check your solution. = 4 a 24 30 1. 5 ANSWER 3 x = 2 – 6 2. 18 ANSWER 4 m 5 = m – 6 3. 18 ANSWER

How much food should the seal be fed per day? Seals Example 3 Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day? Seals SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x 280 = 8 amount of food 100 weight of seal

A 280 pound seal should be fed 22.4 pounds of food per day. Example 3 STEP 2 Solve the proportion. 8 100 x 280 = Write proportion. 8 280 = 100 x Cross products property 2240 = 100x Simplify. 22.4 = x Divide each side by 100. ANSWER A 280 pound seal should be fed 22.4 pounds of food per day.

Guided Practice WHAT IF? In Example 3, suppose the seal weighs 260 pounds. How much food should the seal be fed per day? 4. 20.8 ANSWER

Example 4 Maps Use a metric ruler and the map of Ohio to estimate the distance between Cleveland and Cincinnati. SOLUTION From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters.

Example 4 Write and solve a proportion to find the distance d between the cities. = 4.2 d 1 centimeters 85 kilometers 1 d = 85 4.2 Cross products property d = 357 Simplify. ANSWER The actual distance between Cleveland and Cincinnati is about 357 kilometers.

Guided Practice 5. Use a metric ruler and the map in Example 4 to estimate the distance (in kilometers) between Columbus and Cleveland. about 212.5 km ANSWER Model ships 6. The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. ANSWER about 960 ft

Lesson Quiz Solve the proportion. 10 35 = y 42 1. 13 h = 26 16 2. ANSWER 12 ANSWER 8 9 d + 3 6 17 = 4. 5r 6 = 15 2 3. ANSWER 9 ANSWER 22.5

Lesson Quiz A figurine of a ballerina is based on a scale of 0.5 in:4 in. If the real ballerina used as a model for the figurine is 68 inches tall, what is the height of the figurine? 5. ANSWER 8.5 in.