Question
During the summer, Winnie delivers flowers and Bob babysits for neighbors. To show their earnings, Winnie makes a graph and Bob makes a table. Which statement is true?
Winnie's Wages
A graph has time (hours) on the x-axis, and earnings (dollars) on the y-axis. A line has slope 11.5.
Bob's Wages
Time
(hours) Earnings
(dollars)
3 $46.80
6 $93.60
8 $124.80
Clear Check
Bob earns $12.30
more per hour than Winnie.
Winnie earns $6.15
more per hour than Bob.
Bob earns $4.10
more per hour than Winnie.
Winnie earns $2.05
more per hour than Bob.
Winnie's Wages
A graph has time (hours) on the x-axis, and earnings (dollars) on the y-axis. A line has slope 11.5.
Bob's Wages
Time
(hours) Earnings
(dollars)
3 $46.80
6 $93.60
8 $124.80
Clear Check
Bob earns $12.30
more per hour than Winnie.
Winnie earns $6.15
more per hour than Bob.
Bob earns $4.10
more per hour than Winnie.
Winnie earns $2.05
more per hour than Bob.
Answers
GPT-4o mini
To determine the correct statement about Winnie and Bob's wages, we first need to calculate each of their earnings per hour.
1. **Winnie's Earnings**:
- The slope of the line on Winnie's graph represents her earnings per hour, which is given as 11.5 dollars per hour.
2. **Bob's Earnings**:
- To find Bob's earnings per hour, we can look at the earnings listed in the table.
- We can calculate his earnings per hour by using the given values:
- For 3 hours, he earns $46.80, which gives him an hourly rate of:
\[
\frac{46.80}{3} = 15.60 \, \text{dollars per hour}
\]
- For 6 hours, he earns $93.60, which gives:
\[
\frac{93.60}{6} = 15.60 \, \text{dollars per hour}
\]
- For 8 hours, he earns $124.80, which gives:
\[
\frac{124.80}{8} = 15.60 \, \text{dollars per hour}
\]
- Thus, Bob earns **$15.60 per hour**.
Next, we compare their earnings:
- Winnie earns $11.50 per hour.
- Bob earns $15.60 per hour.
Now let's analyze the statements:
1. **Bob earns $12.30 more per hour than Winnie****.
- Calculation: \( 15.60 - 11.50 = 4.10 \). This statement is false.
2. **Winnie earns $6.15 more per hour than Bob****.
- This statement is false; in fact she earns less.
3. **Bob earns $4.10 more per hour than Winnie****.
- Calculation: \( 15.60 - 11.50 = 4.10 \). This statement is true.
4. **Winnie earns $2.05 more per hour than Bob****.
- This statement is false; in fact she earns less.
Thus, the true statement is:
**Bob earns $4.10 more per hour than Winnie.**
1. **Winnie's Earnings**:
- The slope of the line on Winnie's graph represents her earnings per hour, which is given as 11.5 dollars per hour.
2. **Bob's Earnings**:
- To find Bob's earnings per hour, we can look at the earnings listed in the table.
- We can calculate his earnings per hour by using the given values:
- For 3 hours, he earns $46.80, which gives him an hourly rate of:
\[
\frac{46.80}{3} = 15.60 \, \text{dollars per hour}
\]
- For 6 hours, he earns $93.60, which gives:
\[
\frac{93.60}{6} = 15.60 \, \text{dollars per hour}
\]
- For 8 hours, he earns $124.80, which gives:
\[
\frac{124.80}{8} = 15.60 \, \text{dollars per hour}
\]
- Thus, Bob earns **$15.60 per hour**.
Next, we compare their earnings:
- Winnie earns $11.50 per hour.
- Bob earns $15.60 per hour.
Now let's analyze the statements:
1. **Bob earns $12.30 more per hour than Winnie****.
- Calculation: \( 15.60 - 11.50 = 4.10 \). This statement is false.
2. **Winnie earns $6.15 more per hour than Bob****.
- This statement is false; in fact she earns less.
3. **Bob earns $4.10 more per hour than Winnie****.
- Calculation: \( 15.60 - 11.50 = 4.10 \). This statement is true.
4. **Winnie earns $2.05 more per hour than Bob****.
- This statement is false; in fact she earns less.
Thus, the true statement is:
**Bob earns $4.10 more per hour than Winnie.**