Multistep Tomas makes balloon sculptures at a circus. In 180 he uses 252 balloons to make 36 identical balloon sculptures.

To answer the questions, we will break them down step by step.

a. How many minutes does it take to make one balloon sculpture? How many balloons are used in one sculpture?

1. Finding how many balloons are used in one sculpture:

   • Tomas uses a total of 252 balloons to make 36 sculptures.
   • To find the number of balloons used for one sculpture, we divide the total number of balloons by the number of sculptures: \[ \text{Balloons per sculpture} = \frac{252 \text{ balloons}}{36 \text{ sculptures}} = 7 \text{ balloons per sculpture} \]

2. Finding how long it takes to make one sculpture:

   • Tomas makes 36 sculptures in 180 minutes.
   • To find the time taken to make one sculpture, we divide the total time by the number of sculptures: \[ \text{Time per sculpture} = \frac{180 \text{ minutes}}{36 \text{ sculptures}} = 5 \text{ minutes per sculpture} \]

Summary:

• Balloons used in one sculpture: 7 balloons
• Time to make one sculpture: 5 minutes

b. What is Tomas's unit rate for balloons used per minute?

To find Tomas's unit rate for balloons used per minute, we can calculate the total number of balloons used divided by the total number of minutes taken:

\[ \text{Unit rate} = \frac{252 \text{ balloons}}{180 \text{ minutes}} = \frac{252}{180} \]

Now we simplify that fraction:

\[ \frac{252 \div 36}{180 \div 36} = \frac{7}{5} \text{ balloons per minute} \]

Summary:

• Tomas's unit rate for balloons used per minute: \(\frac{7}{5}\) balloons per minute or 1.4 balloons per minute.

c. Complete the diagram to find out how many balloons he will use in 10 minutes.

We already have the unit rate: Tomas uses \(\frac{7}{5}\) balloons per minute. To find out how many balloons he would use in 10 minutes:

\[ \text{Balloons in 10 minutes} = \text{Unit Rate} \times 10 = \left(\frac{7}{5}\right) \times 10 \]

Calculating that gives:

\[ \text{Balloons in 10 minutes} = \frac{7 \times 10}{5} = \frac{70}{5} = 14 \text{ balloons} \]

Summary:

• Balloons used in 10 minutes: 14 balloons.

Final Results:

a. 5 minutes per sculpture, 7 balloons per sculpture.
b. 1.4 balloons per minute.
c. 14 balloons in 10 minutes.