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Embed code for: 4.5 - Variation
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If an 800 square foot apartment costs $650 per month to rent, what would you expect the monthly rent to be on a 1200 square foot apartment?
7. Explain how to solve a proportion. Illustrate your explanation with an example.
26. 28. Solve for x:
34. The property tax on a house with an assessed value of $520,000 is $7280. Determine the property tax on a house with an assessed value of $650,000, assuming the same tax rate.
35. An alligator’s tail length is proportional to its body length. An alligator with a body length of 4 feet has a tail length of 3.6 feet. What is the tail length of an alligator whose body length is 6 feet?
38. To estimate the number of bass in a lake, wildlife biologists tagged 50 bass and released them in the lake. Later they netted 108 bass and found that 27 of them were tagged. Approximately how many bass are in the lake?
Assignment p. 259-260
Modeling Using Variation
SWBAT solve problems using variation.
Constant of variation
“y varies directly with x”
Example 1: Solving a Direct Variation Problem
B varies directly with W.
W is 160 when B is 5.
Find B when W is 200.
Step 1: Write an equation.
Step 2: Use the given values to find k.
Example 1: continued
Step 3: Substitute the value of k into the equation.
Step 4: Answer the problem’s question.
Think Ink Pair Share
R varies directly with S.
R is 20 when S is 65.
Find R when S is 80.
“y varies inversely with x”
Example 3: Solving an Inverse Variation Problem
P varies inversely with V.
If V = 8 when P = 12,
Find P when V = 22.
Example 3: continued
Q varies inversely with T.
Q is 5 when T is 12.
Find Q when T is 20.
In combined variation, direct and inverse variation occur at the same time.
Direct means multiply (top of fraction)
Inverse means divide (bottom of fraction)
Example 4: Solving a Combined Variation Problem
The owners of Rollerblades Plus determine that the monthly sales, S, of its skates vary directly with its advertising budget, A, and inversely with the price of the skates, P. When $60,000 is spent on advertising and the price of the skates is $40, the monthly sales are 12,000 pairs of rollerblades.
a. Write an equation of variation.
b. Determine monthly sales if the amount of the advertising budget is increased to $70,000.
Make groups of 3 – 4 students.
Work the problem on the sheet given to your group.
When you are done, trade papers with another group.
You need to do 4 out of the 5 problems, so keep track of the numbers!
11. What does it mean if two quantities vary inversely?
18. y varies directly with x. y = 45 when x = 5. Find y when x = 13.
22. y varies inversely with x. y = 6 when x = 3. Find y when x = 9.
25. y varies directly with x and inversely with z. y = 100 when x = 5 and z = 10. Find y when x = 3 and z = 60.
36. The distance that a spring will stretch varies directly as the force applied to the spring. A force of 12 pounds is needed to stretch a spring 9 inches. What force is required to stretch the spring 15 inches?
40. The water temperature of the Pacific Ocean varies inversely as the water’s depth. At a depth of 1000 meters, the water temperature is 4.4°C. What is the water temp at a depth of 5000m?
Page 25919. 21.
Exit Ticket: Write a 2 sentence summary of today’s lesson.