Solve the equation. 1. x = 25 5 6 ANSWER 30 2. (6x + 3) = 14 2 3

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Presentation transcript:

Solve the equation. 1. x = 25 5 6 ANSWER 30 2. (6x + 3) = 14 2 3 ANSWER 3

Solve the equation. 3. – 7 = 12 g 5 ANSWER 95 4. You buy three identical polyester film balloons and a birthday card. The card costs $3.95. Find the cost of each balloon if your total bill before tax was $33.80. ANSWER $9.95

EXAMPLE 1 Write a ratio VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. b. Find the ratio of home matches to all matches. SOLUTION = 7 5 a. home matches away matches 14 10 b. home matches all matches 14 14 + 10 = 24 7 12

EXAMPLE 1 GUIDED PRACTICE for Example 1 Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio. 1. The number of Derek’s CDs to the number of his brother’s CDs. 11 13 ANSWER 2. The number of Derek’s CDs to the number of CDs in the entire collection. 11 24 ANSWER

EXAMPLE 2 Solve a proportion x 30 Solve the proportion 11 6 = . 11 6 x Write original proportion. 11 6 x 30 = Multiply each side by 30. 330 6 = x Simplify. 55 = x Divide.

EXAMPLE 2 GUIDED PRACTICE for Example 2 Solve the proportion. Check your solution. 4 7 w 35 = 3. 20 ANSWER

EXAMPLE 2 GUIDED PRACTICE for Example 2 Solve the proportion. Check your solution. m 12 9 2 = 4. 54 ANSWER

EXAMPLE 2 GUIDED PRACTICE for Example 2 Solve the proportion. Check your solution. 5 9 z 54 = 5. 30 ANSWER

EXAMPLE 3 Solve a multi-step problem ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.

Solve a multi-step problem EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled. x 1029 = 5 Seconds 150 feet STEP 2 Solve the proportion.

Solve a multi-step problem EXAMPLE 3 Solve a multi-step problem 5 150 x 1029 = Write proportion. 5 150 = 1029 x Multiply each side by 1029. 5145 150 = x Simplify. 34.3 = x Use a calculator. ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds.

Daily Homework Quiz Solve the proportion. 32 28 3. = m 14 16 ANSWER 4. A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer. ANSWER 12 3 = x 9 ; 36 color pages

2.7 Solving 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

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

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