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3-5 HW: Pg. 165-167 #6-42eoe, 50-51, 56-57

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56. C 57. D

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Wir2.5 LESSON

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3-6 Solve Proportions Using Cross Products denominator of the other ratio. 2dimensional drawing of an object where dimensions product of numerator of 1 ratio and the of drawing are in proportion to the real object

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Use the cross products property EXAMPLE 1 8 15 = x 6 Solve the proportion =. 8 x 6 15 Cross products property Simplify. 120 = 6x Divide each side by 6. 20 = x The solution is 20. Check by substituting 20 for x in the original proportion. ANSWER Substitute 20 for x. CHECK Cross products property Simplify. Solution checks. 8 20 6 15 = ? 8 15 = 20 6 ? 120 = 120

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

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Write and solve a proportion EXAMPLE 3 x 280 = 8 amount of food 100 weight of seal SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of food with the weight of the seal. 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 STEP 2 Solve the 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.

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EXAMPLE 1 Solve the proportion. Check your solution. GUIDED PRACTICE for Examples 1, 2, and 3 = 4 a 24 30 1. 5 ANSWER 3 x = 2 x– 6 2. 18 ANSWER 4 m 5 = m – 6 3. 30 ANSWER 20.8 ANSWER WHAT IF? In Example 3, suppose the seal weighs 260 pounds. How much food should the seal be fed per day ? 4.

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EXAMPLE 4 Use the scale on a map 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. Write and solve a proportion to find the distance d between the cities. = 3 d 1 centimeters 85 kilometers Cross products property d = 255 Simplify. ANSWERThe actual distance between Cleveland and Cincinnati is about 255 kilometers. 1 d = 85 3

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EXAMPLE 4 Use the scale on a map GUIDED PRACTICE for Example 4 5. Use a metric ruler and the map in Example 4 to estimate the distance (in kilometers) between Columbus and Cleveland. about 144.5 kmANSWER 6.6. 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. Model ships ANSWERabout 960 ft

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Summary How do you solve proportions using cross products? Ans: Cross products of a proportion are equal. Multiply the numerator of each ratio by the denominator of the other ratio and write an equal sign in between the 2 products. Then solve for the variable. If the distance between Columbus and Cincinnati is about 170 km, and the map’s scale is drawn so 1 cm = 85 km. Can you estimate the distance between the two cities? Ans:

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Check Yourself Pg. 171-173 #4-24eoe, 33-34, 44-45 and Quiz Pg. 173 #2-16e

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Ratio and Proportion 7-1.

Ratio and Proportion 7-1.

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