1. Solve Proportions Using Cross Products
Warm Up
Lesson Presentation
Lesson Quiz

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

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. 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.
= 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.

10. 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

11. 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.

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

13. Guided Practice 5.
Use a metric ruler and the map in Example 4 to estimate the distance (in kilometers) between Columbus and Cleveland.
about 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

14. 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

15. 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.