Question

1. multistep tomas makes balloon sculptures at a circus. in 180 minutes, he uses 252 balloons to make 36 identical balloon sculptures.

a. how many minutes does it take to make one balloon sculpture? how many balloons are used in one sculpture?
b. what is tomas’s unit rate for balloons used per minute?
c. complete the diagram to find out how many balloons he will use in 10 minutes.
balloons per minute
10 minutes

Explanation:

Part a

Step 1: Time per sculpture

To find the time to make one sculpture, divide total time by number of sculptures.
Total time = 180 minutes, Number of sculptures = 36.
Formula: $\text{Time per sculpture} = \frac{180}{36}$
Calculation: $\frac{180}{36} = 5$ minutes.

Step 2: Balloons per sculpture

To find balloons per sculpture, divide total balloons by number of sculptures.
Total balloons = 252, Number of sculptures = 36.
Formula: $\text{Balloons per sculpture} = \frac{252}{36}$
Calculation: $\frac{252}{36} = 7$ balloons.

Part b

Step 1: Unit rate (balloons per minute)

Unit rate is total balloons divided by total time.
Total balloons = 252, Total time = 180 minutes.
Formula: $\text{Unit rate} = \frac{252}{180}$
Simplify: $\frac{252 \div 36}{180 \div 36} = \frac{7}{5} = 1.4$ balloons per minute.

Part c

Step 1: Balloons per minute (from part b)

From part b, unit rate is 1.4 balloons per minute (or $\frac{7}{5}$ balloons per minute).

Step 2: Balloons in 10 minutes

Multiply unit rate by 10 minutes.
Formula: $\text{Balloons in 10 minutes} = 1.4 \times 10$ (or $\frac{7}{5} \times 10$)
Calculation: $1.4 \times 10 = 14$ balloons (or $\frac{7}{5} \times 10 = 14$).

Final Answers:

a.

• Time per sculpture: $\boldsymbol{5}$ minutes.
• Balloons per sculpture: $\boldsymbol{7}$ balloons.

b.

• Unit rate: $\boldsymbol{1.4}$ (or $\boldsymbol{\frac{7}{5}}$) balloons per minute.

c.

• Balloons in 10 minutes: $\boldsymbol{14}$ balloons.

Answer:

Part a

Step 1: Time per sculpture

To find the time to make one sculpture, divide total time by number of sculptures.
Total time = 180 minutes, Number of sculptures = 36.
Formula: $\text{Time per sculpture} = \frac{180}{36}$
Calculation: $\frac{180}{36} = 5$ minutes.

Step 2: Balloons per sculpture

To find balloons per sculpture, divide total balloons by number of sculptures.
Total balloons = 252, Number of sculptures = 36.
Formula: $\text{Balloons per sculpture} = \frac{252}{36}$
Calculation: $\frac{252}{36} = 7$ balloons.

Part b

Step 1: Unit rate (balloons per minute)

Unit rate is total balloons divided by total time.
Total balloons = 252, Total time = 180 minutes.
Formula: $\text{Unit rate} = \frac{252}{180}$
Simplify: $\frac{252 \div 36}{180 \div 36} = \frac{7}{5} = 1.4$ balloons per minute.

Part c

Step 1: Balloons per minute (from part b)

From part b, unit rate is 1.4 balloons per minute (or $\frac{7}{5}$ balloons per minute).

Step 2: Balloons in 10 minutes

Multiply unit rate by 10 minutes.
Formula: $\text{Balloons in 10 minutes} = 1.4 \times 10$ (or $\frac{7}{5} \times 10$)
Calculation: $1.4 \times 10 = 14$ balloons (or $\frac{7}{5} \times 10 = 14$).

Final Answers:

a.

• Time per sculpture: $\boldsymbol{5}$ minutes.
• Balloons per sculpture: $\boldsymbol{7}$ balloons.

b.

• Unit rate: $\boldsymbol{1.4}$ (or $\boldsymbol{\frac{7}{5}}$) balloons per minute.

c.

• Balloons in 10 minutes: $\boldsymbol{14}$ balloons.