quiz for lessons 5-1 through 5-6
5-1 ratios
1. a concession stand sold 14 strawberry, 18 banana, 8 grape, and 6 orange fruit drinks during a game. tell whether the ratio of strawberry to orange drinks or the ratio of banana to grape drinks is greater.
5-2 rates
2. shaunti drove 621 miles in 11.5 hours. what was her average speed in miles per hour?
3. a grocery store sells a 7 oz bag of raisins for $1.10 and a 9 oz bag of raisins for $1.46. which size bag has the lowest price per ounce?
5-3 slope and rates of change
tell whether each graph shows a constant or variable rate of change.
if constant, find the slope.
4.
5.
6.
5-4 identifying and writing proportions
find a ratio equivalent to each ratio. then use the ratios to write a proportion.
7. $\frac{10}{16}$
8. $\frac{21}{28}$
9. $\frac{12}{25}$
10. $\frac{40}{48}$
5-5 solving proportions
use cross products to solve each proportion.
11. $\frac{n}{8} = \frac{15}{4}$
12. $\frac{20}{t} = \frac{2.5}{6}$
13. $\frac{6}{11} = \frac{0.12}{z}$
14. $\frac{15}{24} = \frac{x}{10}$
15. one dog year is said to equal 7 human years. if cliff’s dog is 5.5 years old in dog years, what is his dog’s age in human years?
5-6 customary measurements
convert each measure.
16. 7 lb to ounces
17. 15 qt to pints
18. 3 mi to feet
19. 20 fl oz to cups
20. 39 ft to yards
21. 7,000 lb to tons
chapter 5 proportional relationships

Question

Accepted Answer

### Question 1:
# Explanation:
## Step1: Calculate strawberry to orange ratio
Strawberry = 14, Orange = 6. Ratio: $\frac{14}{6} \approx 2.33$
## Step2: Calculate banana to grape ratio
Banana = 18, Grape = 8. Ratio: $\frac{18}{8} = 2.25$
## Step3: Compare the two ratios
$2.33 > 2.25$, so strawberry to orange ratio is greater.
# Answer: The ratio of strawberry to orange drinks is greater.

### Question 2:
# Explanation:
## Step1: Recall average speed formula
Average speed = $\frac{	ext{Distance}}{	ext{Time}}$
## Step2: Substitute values
Distance = 621 miles, Time = 11.5 hours. So, $\frac{621}{11.5} = 54$
# Answer: 54 miles per hour.

### Question 3:
# Explanation:
## Step1: Calculate price per ounce for 7 oz bag
Price = $1.10, Ounces = 7. Price per ounce: $\frac{1.10}{7} \approx 0.157$ dollars per ounce.
## Step2: Calculate price per ounce for 9 oz bag
Price = $1.46, Ounces = 9. Price per ounce: $\frac{1.46}{9} \approx 0.162$ dollars per ounce.
## Step3: Compare the two prices
$0.157 < 0.162$, so 7 oz bag has lower price per ounce.
# Answer: The 7 oz bag of raisins has the lowest price per ounce.

### Question 4:
# Explanation:
## Step1: Identify points
Points: $(-1, 4)$ and $(0, 1)$
## Step2: Use slope formula
Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 4}{0 - (-1)} = \frac{-3}{1} = -3$
## Step3: Determine rate of change
Since slope is constant, rate of change is constant with slope -3.
# Answer: Constant rate of change, slope = -3.

### Question 5:
# Explanation:
## Step1: Analyze the graph
The graph is a curve (not a straight line), so the rate of change is variable.
# Answer: Variable rate of change.

### Question 6:
# Explanation:
## Step1: Identify points
Points: $(-1, 2)$ and $(2, 4)$
## Step2: Use slope formula
Slope $m = \frac{4 - 2}{2 - (-1)} = \frac{2}{3}$
## Step3: Determine rate of change
Since slope is constant, rate of change is constant with slope $\frac{2}{3}$.
# Answer: Constant rate of change, slope = $\frac{2}{3}$.

### Question 7:
# Explanation:
## Step1: Simplify the ratio
$\frac{10}{16}$ can be simplified by dividing numerator and denominator by 2: $\frac{10 \div 2}{16 \div 2} = \frac{5}{8}$
## Step2: Write a proportion
Using equivalent ratio: $\frac{10}{16} = \frac{5}{8}$
# Answer: Equivalent ratio: $\frac{5}{8}$, Proportion: $\frac{10}{16} = \frac{5}{8}$

### Question 8:
# Explanation:
## Step1: Simplify the ratio
$\frac{21}{28}$ can be simplified by dividing numerator and denominator by 7: $\frac{21 \div 7}{28 \div 7} = \frac{3}{4}$
## Step2: Write a proportion
Using equivalent ratio: $\frac{21}{28} = \frac{3}{4}$
# Answer: Equivalent ratio: $\frac{3}{4}$, Proportion: $\frac{21}{28} = \frac{3}{4}$

### Question 9:
# Explanation:
## Step1: Find an equivalent ratio
Multiply numerator and denominator by 2: $\frac{12 	imes 2}{25 	imes 2} = \frac{24}{50}$
## Step2: Write a proportion
Using equivalent ratio: $\frac{12}{25} = \frac{24}{50}$
# Answer: Equivalent ratio: $\frac{24}{50}$, Proportion: $\frac{12}{25} = \frac{24}{50}$

### Question 10:
# Explanation:
## Step1: Simplify the ratio
$\frac{40}{48}$ can be simplified by dividing numerator and denominator by 8: $\frac{40 \div 8}{48 \div 8} = \frac{5}{6}$
## Step2: Write a proportion
Using equivalent ratio: $\frac{40}{48} = \frac{5}{6}$
# Answer: Equivalent ratio: $\frac{5}{6}$, Proportion: $\frac{40}{48} = \frac{5}{6}$

### Question 11:
# Explanation:
## Step1: Cross - multiply
$\frac{n}{8} = \frac{15}{4}$ gives $4n = 8 	imes 15$
## Step2: Solve for n
$4n = 120$, so $n = \frac{120}{4} = 30$
# Answer: $n = 30$

### Question 12:
# Explanation:
## Step1: Cross - multiply
$\frac{20}{t} = \frac{2.5}{6}$ gives $2.5t = 20 	imes 6$
## Step2: Solve for t
$2.5t = 120$, so $t = \frac{120}{2.5} = 48$
# Answer: $t = 48$

### Question 13:
# Explanation:
## Step1: Cross - multiply
$\frac{6}{11} = \frac{0.12}{z}$ gives $6z = 11 	imes 0.12$
## Step2: Solve for z
$6z = 1.32$, so $z = \frac{1.32}{6} = 0.22$
# Answer: $z = 0.22$

### Question 14:
# Explanation:
## Step1: Cross - multiply
$\frac{15}{24} = \frac{x}{10}$ gives $24x = 15 	imes 10$
## Step2: Solve for x
$24x = 150$, so $x = \frac{150}{24} = 6.25$
# Answer: $x = 6.25$

### Question 15:
# Explanation:
## Step1: Set up proportion
Let $x$ be dog's age in human years. $\frac{1}{7} = \frac{5.5}{x}$ (1 dog year = 7 human years)
## Step2: Cross - multiply
$x = 5.5 	imes 7 = 38.5$
# Answer: 38.5 human years.

### Question 16:
# Explanation:
## Step1: Recall conversion factor
1 lb = 16 ounces
## Step2: Convert 7 lb to ounces
$7 	imes 16 = 112$ ounces
# Answer: 112 ounces.

### Question 17:
# Explanation:
## Step1: Recall conversion factor
1 qt = 2 pints
## Step2: Convert 15 qt to pints
$15 	imes 2 = 30$ pints
# Answer: 30 pints.

### Question 18:
# Explanation:
## Step1: Recall conversion factor
1 mi = 5280 feet
## Step2: Convert 3 mi to feet
$3 	imes 5280 = 15840$ feet
# Answer: 15840 feet.

### Question 19:
# Explanation:
## Step1: Recall conversion factor
1 cup = 8 fl oz
## Step2: Convert 20 fl oz to cups
$\frac{20}{8} = 2.5$ cups
# Answer: 2.5 cups.

### Question 20:
# Explanation:
## Step1: Recall conversion factor
1 yard = 3 feet
## Step2: Convert 39 ft to yards
$\frac{39}{3} = 13$ yards
# Answer: 13 yards.

### Question 21:
# Explanation:
## Step1: Recall conversion factor
1 ton = 2000 lb
## Step2: Convert 7000 lb to tons
$\frac{7000}{2000} = 3.5$ tons
# Answer: 3.5 tons.

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QUESTION IMAGE

Question

Explanation:

Question 1:

Step1: Calculate strawberry to orange ratio

Step2: Calculate banana to grape ratio

Step3: Compare the two ratios

Step1: Recall average speed formula

Step2: Substitute values

Step1: Calculate price per ounce for 7 oz bag

Step2: Calculate price per ounce for 9 oz bag

Step3: Compare the two prices

Answer:

Question 2: