Unit 3

Ratios and Proportional Relationships

Name ___________________________ Class___________

Unit RatesUnit Rate ____________________________________________________________________

Examples

a. $300 for 6 hours b. 220 miles on 8 gallons c. 24 miles in 4 hours

d. The prices of 3 different bags of dog food are given in the table. Which size bag has the lowestprice per pound rounded to the nearest cent?

What is the difference between the 40 lb. and 8 lb bag rates, in price per pound?

e. Tito wants to buy some peanut butter to donate to the local food pantry. Tito wants to buy as much peanut butter as possible. Which brand should he buy?

f. CD Express offers 4 CDs for $60. Music Place offers 6 CDs for $75. Which store offers the better buy? What is the difference in price per CD?

g. After 3.5 hours, Pasha had traveled 217 miles. If she travels at a constant speed, how far will she have traveled after 4 hours?

h. Write 5 pounds for $2.49 as a unit rate. Round to the nearest hundredth.

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Rounding Money

To the nearest penny - __________________________ $12. 467 = $12.47 but $12.464 = $12.46

1. 9.275 __________ 2. 110.458__________ 3. .751__________

4. .3445__________ 5. 2.146__________ 6. 2.1418__________

7. 515.497__________ 8. 264.997__________ 9. 1.848__________

10. 10.10175__________ 11. 111.119__________ 12. .12511__________

13. Quaker Cereal Bars cost $3.79 for 10.4 ounces. How much is she paying per ounce?

14. Fiber One costs $4.99 for 16.2 ounces of cereal. How much is she paying per ounce?

15. Cinnamon Toast Crunch costs $3.89 for 12.8 ounces of cereal. How much is she paying per oz?

16. Multigrain Cheerios cost $4.39 for 9 ounces of cereal. How much is she paying per ounce?

Write the unit rate on the line. Circle the better buy.

1. 3 batteries for $4.80__________ 12 batteries for $14.76__________

2. 22 staplers for $330__________ 4 staplers for $80__________

3. 5 calculators for $105__________ $552 for 24 calculators__________

4. 18 pens for $6.84__________ 30 pens for $8.40__________

5. $99 for 11 books__________ 29 books for $203__________

6. $15.98 for 34 liters of soda__________ $4.68 for 12 liters of soda__________

7. 39 pens for $8.19__________ 11 pens for $3.41__________

8. 3 liters of soda for $1.89__________ 10 liters of soda for $6.40__________

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Complex Fractions

a. 223

b. 613

c. 237

d.

3414

Unit Rate with Fractions

a. Josiah can jog 113 miles in

14 hour. Find his average speed in miles per hour.

b. Tia is painting her house. She paints 2412 square feet in

34 hour. At this rate, how many

square feet can she paint each hour?

c. Mr. Ito is spreading mulch in his yard. He spreads 423 square yards in 2 hours. How many

square yards can he mulch per hour?

d. Aubrey can walk 412 miles in 1

12 hours. Find her average speed in miles per hour.

e. Pep Club members are making spirit buttons. They make 490 spirit buttons in 3 ½ hours. Find the number of buttons the Pep Club makes per hour.

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f. 1834

g. 364

h.

1314

Proportional RelationshipsTwo quantities are proportional if __________________________________________________

Equivalent ratios ____________________________________________

Examples

a. What is the cost per adult ticket at the Amusement Park? What is the price for 18 adult tickets?

b. Rafael pays $550 in rent each month. Which table best represents the relationship between m, the number of months, and r, the amount he pays in rent for that length of time?

c. Is the cost of downloading a movie proportional to the number of movies downloaded?

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d. Mrs. Pardue wants to purchase some apples. She compared prices from several different on-line grocers. Which grocery store’s price table is based on a constant unit price?

e. You have been hired by your neighbors to babysit their children on Friday night. You are paid $8 per hour. Complete the table relating your pay to the number of hours you worked.

Based on the table you completed, is pay proportional to hours work? How do you know?

Show TWO ways you may use the table to determine the pay for 20 hours:

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f. Is the amount in a savings account in the table below proportional to the number of months of saving? Explain your answer

Constant of Proportionality – Tables/GraphsDetermine the constant of proportionality for each table. Express your answer as y=kx

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Constant Rate of Changevs.

Proportional RelationshipStraight lines have a __________________________________________________________

Proportional Relationships have _________________________________________________

1. Create a table for the graph below. Is the number of British Pounds proportional to the number of US Dollars?

2. Rudolph starts out the week with $10 in cash and makes $8.50 an hour working at his father’s store. Fill in the table below for the amount of cash for the given hours.

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Is this relationship proportional? How can you tell by looking at a graph?

3. At 2 P.M., the level of the water in the pool was 10 feet. At 6 P.M., the level of water was 2 feet. Find the constant rate of change of the water level over time.

4. JoAnne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months, there is $300 in the account. Find the constant rate of change of the account each month.

5. The temperature at noon was 88°F. By 4 P.M., the temperature was 72°F. Find the constant rate of change of the temperature per hour.

6. Label each table with the appropriate Plan based on the graph below.

____________________ _____________________

Which plan has a cost proportional to the number of texts? Explain.

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SlopeSlope measures the _____________________________________________________________

1. 2.

3. 4.

5. 6.

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7. GO-KARTS The graph shows the average speed of two go-karts in a race.

What does the point (2, 20) represent on the graph?

What does the point (1, 12) represent on the graph?

What does the slope of each line represent? Which car is traveling faster?

Direct Variation1. Which equation is not an example of a direct variation?

a. y=73x+1 b. y= 5

16x c. y=4 x d. y=−9 x

2. Which equation is not an example of a direct variation?

a. y=x b. 2 x+3 y=0 c. y=12x d. 5 x+6 y=30

Name the constant of variations (k) for each equation.

3. y=5 x 4. y=12x 5. y=−2

3x

If y varies directly with x, write an equation for the direct variation. Then find each value

6. If y = 21 when x = 3, find x when y = 42.

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7. If y = 36 when x = 4, find y when x = 11.

8. If y = 9 when x = 3/2, find y when x = 2.

Linear Equations

The graph represents the cost of Gasoline at $3 per gallon. Write an equation for the graph.

Write an equation that represents the cost of gasoline at $3 per gallon and a drink that costs $2. How is this different from the graphs to the left?

Non-proportional linear functions can be written in the form _______________

This is called the __________________________.

When an equation is written in this form, m is the _______________and b is the __________________.

The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis.

Examples

State the slope and the y-intercept of the graph of each equation

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1. y=2x−4 2. y=−3x+3 3. y=14x−6

4. y=2x 5. y=−x 6. y=12x+1

On a separate sheet of paper make a table for each of the above linear equations. Use equation to fill in the table below for the y-values. Use a piece of graph paper to graph the lines for each linear equation.

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x y-2-10123

Finding the Slope

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Find the slope of the line that passes through the points (-1, 4) and (1, -2)

Find the slope both algebraically and graphically.

Graph the points and connect the dots using a straight edge.

1. (0, 2) and (4, 3) 2. (-4, 6) and (5,3)

3. (2, -1) and (7, -1) 4. (-5, 1) and (-4, 7)

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Graphing a Line

Graph y=−32x−1 using the slope and y-intercept.

Step 1: Find the slope _____ and y-intercept ________

Step 2: Graph the y-intercept.

Step 3: Use the slope to locate a second point on the line.

Practice

a. y=x+3 b. y=12x−1 c. y=

−43x+2

The Student Government is selling spirit T-shirts during spirit week. It costs $20 for the design and $5 to print each shirt. The cost y to print x shirts is given by y=5 x+20

Graph the equation to find the number of shirts that can be printed for $50

Step 1 – Plot the point (0,20) to represent the $20 design fee.

Step 2 – Locate another point up 5 and to the right 1.

Step 3 – Connect the points and continue the line through the rest of the graph to locate the x-coordinate when the y-coordinate is 50.

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Is this a proportional relationship? Why or why not?

Describe what the slope and y-intercept represent.

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