2.7 solve proportions using cross products you will 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?
Warm-Up ExercisesUse the cross products propertyEXAMPLE 1
Write original proportion.
8 15 = x 6
Solve the proportion = .8 x
615
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
=8 x
615
Warm-Up ExercisesUse the cross products propertyEXAMPLE 1
Substitute 20 for x.
CHECK
Cross products property
Simplify. Solution checks.
820
615
=?
8 15 = 20 6?
120 = 120
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
What is the value of x in the proportion = ?4x
83x –
A – 6 B – 3 C 3 D 6
SOLUTION
4x =
8x – 3
Write original proportion.
Cross products property4(x – 3) = x 8
4x – 12 = 8x Simplify.
Subtract 4x from each side. –12 = 4x
Divide each side by 4. –3 = x
Warm-Up Exercises
EXAMPLE 2 Standardized Test Practice
The value of x is –3. The correct answer is B.
ANSWER
A B C D
Warm-Up ExercisesWrite and solve a proportion
EXAMPLE 3
x280
= 8 amount of food100 weight of seal
SOLUTION
STEP 1Write 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
Warm-Up ExercisesWrite and solve a proportion
EXAMPLE 3
STEP 2Solve the proportion.
8100
x280
= 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 perday.
Warm-Up ExercisesEXAMPLE 1
Solve the proportion. Check your solution.
GUIDED PRACTICE for Examples 1, 2, and 3
=4 a
2430
1.
5ANSWER
Warm-Up ExercisesEXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3
3x =
2x – 6
2.
18ANSWER
Solve the proportion. Check your solution.
Warm-Up ExercisesEXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3
4m5 =
m – 6 3.
18ANSWER
Solve the proportion. Check your solution.
Warm-Up Exercises
EXAMPLE 3GUIDED PRACTICE for Examples 1, 2, and 3
20.8ANSWER
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.
Warm-Up ExercisesEXAMPLE 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.
Warm-Up ExercisesEXAMPLE 4 Use the scale on a map
Write and solve a proportion to find the distance d between the cities.
=4.2 d
1 centimeters85 kilometers
Cross products property
d = 357 Simplify.
ANSWER
The actual distance between Cleveland and Cincinnati is about 357 kilometers.
1 d = 85 4.2
Warm-Up ExercisesEXAMPLE 4 Use the scale on a mapGUIDED 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 kmANSWER
Warm-Up ExercisesEXAMPLE 4 Use the scale on a mapGUIDED PRACTICE for Example 4
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
ANSWER about 960 ft
Warm-Up ExercisesDaily Homework Quiz
10 35
=y
421.
13 h
= 26 16
2.
ANSWER 12
ANSWER 8
5r 6
= 15 2
3.
ANSWER 9
Warm-Up ExercisesDaily Homework Quiz
9d + 3
617
=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.
• You will solve proportions using cross products.
• Essential Question: How do you solve proportions using cross products?
•Cross products of a proportionare equal.• The scale of a scale drawing ormodel relates the drawing’s ormodel’s dimensions to the actualdimensions.
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.