1. jenny packaged 108 eggs in 9 cartons. write this statement as a rate.
2. anna maria read 40 pages in 60 minutes. what is her unit rate in pages per minute?
3. a bathroom shower streams 5 gallons of water in 2 minutes.
a. find the unit rate for gallons per minute and describe it in words.
b. find the unit rate for minutes per gallon and describe it in words.
in 4 and 5, find the value of n.
4.
| miles | 45 | 135 |
| hours | 4 | n |
5. a graph with pounds on one axis (marked 0, 1, n) and cost ($) on the other (marked 0, 2, 5).

Question

1. jenny packaged 108 eggs in 9 cartons. write this statement as a rate.
2. anna maria read 40 pages in 60 minutes. what is her unit rate in pages per minute?
3. a bathroom shower streams 5 gallons of water in 2 minutes.
   a. find the unit rate for gallons per minute and describe it in words.
   b. find the unit rate for minutes per gallon and describe it in words.
in 4 and 5, find the value of n.
4.
| miles | 45 | 135 |
| hours | 4 | n |
5. a graph with pounds on one axis (marked 0, 1, n) and cost ($) on the other (marked 0, 2, 5).

Accepted Answer

### Problem 1 (Jenny's Eggs)
# Explanation:
## Step1: Identify the quantities
Jenny packaged 108 eggs in 9 cartons. A rate is a ratio of two quantities. So the rate is eggs to cartons.
## Step2: Write the rate
The rate is $\frac{108 	ext{ eggs}}{9 	ext{ cartons}}$. To simplify, we can also write it as a unit rate by dividing 108 by 9. $108\div9 = 12$. So the rate is 12 eggs per carton.
# Answer:
The rate is $\frac{108 	ext{ eggs}}{9 	ext{ cartons}}$ or 12 eggs per carton.

### Problem 2 (Anna Maria's Reading)
# Explanation:
## Step1: Recall unit rate formula
Unit rate for pages per minute is $\frac{	ext{Number of pages}}{	ext{Number of minutes}}$.
## Step2: Substitute values
Number of pages = 40, Number of minutes = 60. So unit rate = $\frac{40}{60}$. Simplify the fraction: divide numerator and denominator by 20, we get $\frac{2}{3}$.
# Answer:
Her unit rate is $\frac{2}{3}$ pages per minute.

### Problem 3 (Shower Water)
#### Part a: Gallons per minute
# Explanation:
## Step1: Unit rate formula
Unit rate (gallons per minute) = $\frac{	ext{Gallons of water}}{	ext{Minutes}}$.
## Step2: Substitute values
Gallons = 5, Minutes = 2. So unit rate = $\frac{5}{2}= 2.5$.
## Step3: Describe the rate
The shower streams 2.5 gallons of water per minute.
# Answer:
The unit rate is 2.5 gallons per minute. The shower streams 2.5 gallons of water in one minute.

#### Part b: Minutes per gallon
# Explanation:
## Step1: Unit rate formula
Unit rate (minutes per gallon) = $\frac{	ext{Minutes}}{	ext{Gallons of water}}$.
## Step2: Substitute values
Minutes = 2, Gallons = 5. So unit rate = $\frac{2}{5}= 0.4$.
## Step3: Describe the rate
It takes 0.4 minutes (or 24 seconds) to stream 1 gallon of water.
# Answer:
The unit rate is 0.4 minutes per gallon. It takes 0.4 minutes to stream 1 gallon of water.

### Problem 4 (Miles and Hours)
# Explanation:
## Step1: Recognize proportionality
The table shows a proportional relationship between miles and hours. So the ratio of miles to hours should be constant.
## Step2: Set up the proportion
$\frac{45 	ext{ miles}}{4 	ext{ hours}}=\frac{135 	ext{ miles}}{n 	ext{ hours}}$.
## Step3: Cross - multiply
$45	imes n=135	imes4$.
## Step4: Solve for n
$45n = 540$. Divide both sides by 45: $n=\frac{540}{45}=12$.
# Answer:
The value of $n$ is 12.

### Problem 5 (Pounds and Cost)
# Explanation:
## Step1: Recognize proportional relationship
From the graph, when pounds = 1, cost = 2. So the cost per pound is $2\div1 = 2$ dollars per pound. Let the cost for $n$ pounds be 5 dollars. Since cost and pounds are proportional, $\frac{	ext{Cost}}{	ext{Pounds}}=	ext{Constant rate}$. The constant rate is 2 (dollars per pound). So if cost is 5 dollars, then $	ext{Pounds}=\frac{	ext{Cost}}{	ext{Rate}}$.
## Step2: Calculate n
$n=\frac{5}{2}=2.5$.
# Answer:
The value of $n$ is 2.5.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1 (Jenny's Eggs)

Step1: Identify the quantities

Step2: Write the rate

Step1: Recall unit rate formula

Step2: Substitute values

Step1: Unit rate formula

Step2: Substitute values

Step3: Describe the rate

Answer:

Problem 2 (Anna Maria's Reading)