Question
At a carnival game, it cost Francisco $8 to toss 26 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Dollars Tosss
4
8 26
52
Dollars Tosss
4
8 26
52
Answers
GPT-4o mini
To create a table of equivalent ratios for Francisco's ring toss game, we start by noting that it costs him $8 for 26 tosses. This gives us a rate of:
\[
\text{Cost per toss} = \frac{8 \text{ dollars}}{26 \text{ tosses}} \approx 0.3077 \text{ dollars per toss}
\]
Using this rate, we can calculate the cost and number of tosses for various amounts. Let's fill out the table:
| Dollars | Tosses |
|---------|--------|
| 4 | ? |
| 8 | 26 |
| ? | 52 |
### Finding Values:
1. **For $4**:
Since $8 corresponds to 26 tosses, we can set up a proportion for $4:
\[
\frac{4}{x} = \frac{8}{26}
\]
Cross-multiplying gives:
\[
4 \times 26 = 8 \times x \implies 104 = 8x \implies x = \frac{104}{8} = 13
\]
So when Francisco spends $4, he can toss **13 rings**.
2. **For 52 Tosses**:
Using the same proportion:
\[
\frac{8}{26} = \frac{y}{52}
\]
Cross-multiplying gives:
\[
8 \times 52 = 26y \implies 416 = 26y \implies y = \frac{416}{26} = 16
\]
Thus, if Francisco tosses **52 rings**, it will cost him **$16**.
### Completed Table:
Now we can fill in the complete table:
| Dollars | Tosses |
|---------|--------|
| 4 | 13 |
| 8 | 26 |
| 16 | 52 |
### Plotting the Points:
Next, we'll plot the points corresponding to the ratios in the table on a coordinate graph where the x-axis represents the number of tosses and the y-axis represents the dollars spent.
- Point for (13, 4)
- Point for (26, 8)
- Point for (52, 16)
### Coordinate Axes:
- **x-axis**: Tosses (0 to 60)
- **y-axis**: Dollars (0 to 20)
Plotting these points on the graph should give a straight line, indicating the linear relationship between the number of tosses and the cost.
This completes the table of equivalent ratios and gives you the information needed to plot the points.
\[
\text{Cost per toss} = \frac{8 \text{ dollars}}{26 \text{ tosses}} \approx 0.3077 \text{ dollars per toss}
\]
Using this rate, we can calculate the cost and number of tosses for various amounts. Let's fill out the table:
| Dollars | Tosses |
|---------|--------|
| 4 | ? |
| 8 | 26 |
| ? | 52 |
### Finding Values:
1. **For $4**:
Since $8 corresponds to 26 tosses, we can set up a proportion for $4:
\[
\frac{4}{x} = \frac{8}{26}
\]
Cross-multiplying gives:
\[
4 \times 26 = 8 \times x \implies 104 = 8x \implies x = \frac{104}{8} = 13
\]
So when Francisco spends $4, he can toss **13 rings**.
2. **For 52 Tosses**:
Using the same proportion:
\[
\frac{8}{26} = \frac{y}{52}
\]
Cross-multiplying gives:
\[
8 \times 52 = 26y \implies 416 = 26y \implies y = \frac{416}{26} = 16
\]
Thus, if Francisco tosses **52 rings**, it will cost him **$16**.
### Completed Table:
Now we can fill in the complete table:
| Dollars | Tosses |
|---------|--------|
| 4 | 13 |
| 8 | 26 |
| 16 | 52 |
### Plotting the Points:
Next, we'll plot the points corresponding to the ratios in the table on a coordinate graph where the x-axis represents the number of tosses and the y-axis represents the dollars spent.
- Point for (13, 4)
- Point for (26, 8)
- Point for (52, 16)
### Coordinate Axes:
- **x-axis**: Tosses (0 to 60)
- **y-axis**: Dollars (0 to 20)
Plotting these points on the graph should give a straight line, indicating the linear relationship between the number of tosses and the cost.
This completes the table of equivalent ratios and gives you the information needed to plot the points.
At a carnival game, it cost Francisco $8 to toss 26 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Dollars Tosss
4
8 26
52
Dollars Tosss
4
8 26
52