Question

A football team was awarded a grant to purchase new helmets. For every 4 players, they can purchase 10 new helmets.

Complete the equivalent ratios in the table to help plan out the number of helmets to purchase.

Fill in the blanks
Number of Players Number of Helmets
4 10
Select Answer

18
30
20
Select Answer

60
24
Select Answer

Select Answer

Submit

You can ear

Answer 1

To complete the equivalent ratios based on the information that for every 4 players, the team can purchase 10 new helmets, we can set up the ratios as follows:

1. The ratio of players to helmets is given as \( \frac{4 \text{ players}}{10 \text{ helmets}} \).

To find the number of helmets for different numbers of players, we can use the principle of proportions.

For **18 players**:
- Set up the proportion:
\[
\frac{4 \text{ players}}{10 \text{ helmets}} = \frac{18 \text{ players}}{x \text{ helmets}}
\]
- Cross-multiply and solve for \( x \):
\[
4x = 180 \implies x = \frac{180}{4} = 45 \text{ helmets}
\]

For **24 players**:
- Set up the proportion:
\[
\frac{4 \text{ players}}{10 \text{ helmets}} = \frac{24 \text{ players}}{y \text{ helmets}}
\]
- Cross-multiply and solve for \( y \):
\[
4y = 240 \implies y = \frac{240}{4} = 60 \text{ helmets}
\]

For **30 players**:
- Set up the proportion:
\[
\frac{4 \text{ players}}{10 \text{ helmets}} = \frac{30 \text{ players}}{z \text{ helmets}}
\]
- Cross-multiply and solve for \( z \):
\[
4z = 300 \implies z = \frac{300}{4} = 75 \text{ helmets}
\]

So in summary, here’s how the table would look:

| Number of Players | Number of Helmets |
|-------------------|-------------------|
| 4 | 10 |
| 18 | 45 |
| 20 | 50 | (calculated as \( 20 \div 4 \times 10 = 50 \))
| 24 | 60 |
| 30 | 75 |

You can fill in the table like this:

1. **For 18 players**: **45 helmets**
2. **For 20 players**: **50 helmets**
3. **For 24 players**: **60 helmets**
4. **For 30 players**: **75 helmets**

Please let me know if you need more assistance!