Question
Unit Rates and proportions unit test
Answers
GPT-4o mini
Sure! Here’s a practice unit test on unit rates and proportions that covers different types of problems commonly found in this topic.
### Unit Rates and Proportions Unit Test
**Instructions:** Provide your answer to each question. Show your work where applicable.
---
**1. Unit Rates:**
A car travels 300 miles using 10 gallons of gas. What is the unit rate of miles per gallon?
**2. Proportions:**
If 5 apples cost $2, how much would 8 apples cost? Set up a proportion and solve.
**3. Unit Rates:**
A recipe calls for 3 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?
**4. Proportions:**
A map scale shows that 1 inch represents 50 miles. If two cities are 4 inches apart on the map, what is the actual distance between them in miles?
**5. Unit Rates:**
A store sells 6 pounds of oranges for $4. How much do you pay per pound?
**6. Proportions:**
If a car can travel 300 miles with 15 gallons of gas, how far can it travel with 25 gallons of gas? Set up a proportion and solve.
**7. Unit Rates:**
You can buy 3 notebooks for $5. What is the unit price per notebook?
**8. Proportions:**
In a class of 30 students, 18 are girls. If a new student joins, making the total number of students 31, how many girls would be in the class if the same ratio is maintained?
---
### Answer Key
**1.** Unit rate = 300 miles / 10 gallons = 30 miles per gallon.
**2.** Set up a proportion:
\[
\frac{5 \text{ apples}}{2 \text{ dollars}} = \frac{8 \text{ apples}}{x \text{ dollars}}
\]
Cross multiply and solve:
\[
5x = 16 \implies x = \frac{16}{5} = 3.20
\]
So, 8 apples cost $3.20.
**3.** Find the unit rate first:
\[
3 \text{ cups} / 12 \text{ cookies} = 0.25 \text{ cups per cookie}
\]
Then for 30 cookies:
\[
0.25 \text{ cups per cookie} \times 30 \text{ cookies} = 7.5 \text{ cups}
\]
So, you need 7.5 cups of flour.
**4.** Distance = 4 inches × 50 miles/inch = 200 miles.
**5.** Unit price = $4 / 6 lbs = $0.67 per pound.
**6.** Set up a proportion:
\[
\frac{300 \text{ miles}}{15 \text{ gallons}} = \frac{x \text{ miles}}{25 \text{ gallons}}
\]
Cross multiply and solve:
\[
15x = 7500 \implies x = 500
\]
So, the car can travel 500 miles with 25 gallons of gas.
**7.** Unit price = $5 / 3 notebooks = $1.67 per notebook.
**8.** Maintain the same ratio of girls (18/30).
Setting up the proportion when the total class size is 31:
\[
\frac{18}{30} = \frac{y}{31}
\]
Cross multiply and solve for y:
\[
18 \cdot 31 = 30y \implies 558 = 30y \implies y = 18.6
\]
Since y must be a whole number, there would still be 18 girls in this new setup if the ratio could not be maintained exactly.
---
Feel free to adjust the questions or the answer key as per your requirements!
### Unit Rates and Proportions Unit Test
**Instructions:** Provide your answer to each question. Show your work where applicable.
---
**1. Unit Rates:**
A car travels 300 miles using 10 gallons of gas. What is the unit rate of miles per gallon?
**2. Proportions:**
If 5 apples cost $2, how much would 8 apples cost? Set up a proportion and solve.
**3. Unit Rates:**
A recipe calls for 3 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?
**4. Proportions:**
A map scale shows that 1 inch represents 50 miles. If two cities are 4 inches apart on the map, what is the actual distance between them in miles?
**5. Unit Rates:**
A store sells 6 pounds of oranges for $4. How much do you pay per pound?
**6. Proportions:**
If a car can travel 300 miles with 15 gallons of gas, how far can it travel with 25 gallons of gas? Set up a proportion and solve.
**7. Unit Rates:**
You can buy 3 notebooks for $5. What is the unit price per notebook?
**8. Proportions:**
In a class of 30 students, 18 are girls. If a new student joins, making the total number of students 31, how many girls would be in the class if the same ratio is maintained?
---
### Answer Key
**1.** Unit rate = 300 miles / 10 gallons = 30 miles per gallon.
**2.** Set up a proportion:
\[
\frac{5 \text{ apples}}{2 \text{ dollars}} = \frac{8 \text{ apples}}{x \text{ dollars}}
\]
Cross multiply and solve:
\[
5x = 16 \implies x = \frac{16}{5} = 3.20
\]
So, 8 apples cost $3.20.
**3.** Find the unit rate first:
\[
3 \text{ cups} / 12 \text{ cookies} = 0.25 \text{ cups per cookie}
\]
Then for 30 cookies:
\[
0.25 \text{ cups per cookie} \times 30 \text{ cookies} = 7.5 \text{ cups}
\]
So, you need 7.5 cups of flour.
**4.** Distance = 4 inches × 50 miles/inch = 200 miles.
**5.** Unit price = $4 / 6 lbs = $0.67 per pound.
**6.** Set up a proportion:
\[
\frac{300 \text{ miles}}{15 \text{ gallons}} = \frac{x \text{ miles}}{25 \text{ gallons}}
\]
Cross multiply and solve:
\[
15x = 7500 \implies x = 500
\]
So, the car can travel 500 miles with 25 gallons of gas.
**7.** Unit price = $5 / 3 notebooks = $1.67 per notebook.
**8.** Maintain the same ratio of girls (18/30).
Setting up the proportion when the total class size is 31:
\[
\frac{18}{30} = \frac{y}{31}
\]
Cross multiply and solve for y:
\[
18 \cdot 31 = 30y \implies 558 = 30y \implies y = 18.6
\]
Since y must be a whole number, there would still be 18 girls in this new setup if the ratio could not be maintained exactly.
---
Feel free to adjust the questions or the answer key as per your requirements!