2.7 Solve Proportions Using Cross Products

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2.7 Solve Proportions Using Cross Products You will solve proportions using cross products. Essential Question: How do you solve proportions using cross products?

Use the cross products property EXAMPLE 1 Use the cross products property Solve the proportion = . 8 x 6 15 = 8 x 6 15 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

Use the cross products property EXAMPLE 1 Use the cross products property CHECK 8 20 6 15 = ? Substitute 20 for x. 8 15 = 20 6 ? Cross products property 120 = 120 Simplify. Solution checks.

Standardized Test Practice EXAMPLE 2 Standardized Test Practice 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.

EXAMPLE 2 Standardized Test Practice The value of x is –3. The correct answer is B. ANSWER A B C D

Write and solve a proportion EXAMPLE 3 Write and solve a proportion 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

Write and solve a proportion EXAMPLE 3 Write and solve a proportion 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.

EXAMPLE 1 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the proportion. Check your solution. = 4 a 24 30 1. 5 ANSWER

EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the proportion. Check your solution. 3 x = 2 – 6 2. 18 ANSWER

EXAMPLE 2 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the proportion. Check your solution. 4 m 5 = m – 6 3. 18 ANSWER

EXAMPLE 3 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the proportion. Check your solution. 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 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.

Use the scale on a map 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.

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 212.5 km ANSWER

EXAMPLE 4 Use the scale on a map GUIDED PRACTICE for Example 4 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

Daily Homework Quiz 10 35 = y 42 1. ANSWER 12 13 h = 26 16 2. ANSWER 8 5r 6 = 15 2 3. ANSWER 9

Daily Homework Quiz 9 d + 3 6 17 = 4. ANSWER 22.5 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.

Essential Question: How do you solve proportions using cross products? You will solve proportions using cross products. Cross products of a proportion are equal. • The scale of a scale drawing or model relates the drawing’s or model’s dimensions to the actual dimensions. To use cross products, multiply the numerator of each ratio by the denominator of the other ratio, and write an equal sign between the two products. Then solve for the variable.