Question
Salary in Company 1
Hours Worked (x) Dollars Earned (y)
5 112.50
10 185
15 257.50
20 330
Amy is applying for a job in two companies. The given table shows the salary in dollars (y) that Company 1 is offering if she works x hours. Company 2 is offering $12.50 per hour plus a bonus of $80. If she plans to work 40 hours each week, in which company will she earn more money in a week and by how much more?
Responses
A She will earn $20 more in Company 1.She will earn $20 more in Company 1.
B She will earn $40 more in Company 1.She will earn $40 more in Company 1.
C She will earn $20 more in Company 2.She will earn $20 more in Company 2.
D She will earn $40 more in Company 2.
Hours Worked (x) Dollars Earned (y)
5 112.50
10 185
15 257.50
20 330
Amy is applying for a job in two companies. The given table shows the salary in dollars (y) that Company 1 is offering if she works x hours. Company 2 is offering $12.50 per hour plus a bonus of $80. If she plans to work 40 hours each week, in which company will she earn more money in a week and by how much more?
Responses
A She will earn $20 more in Company 1.She will earn $20 more in Company 1.
B She will earn $40 more in Company 1.She will earn $40 more in Company 1.
C She will earn $20 more in Company 2.She will earn $20 more in Company 2.
D She will earn $40 more in Company 2.
Answers
GPT-4o mini
To determine which company Amy will earn more from working 40 hours, we first need to calculate her earnings from both companies.
**Earnings from Company 1:**
From the data given, we can see that the salary increases with hours worked. Since we have data for up to 20 hours, we can observe the pattern or derive the equation.
Let's find the rate per hour in Company 1.
Calculating the change in earnings:
- From 0 to 5 hours: \( 112.50 - 0 = 112.50 \) for 5 hours.
- From 5 to 10 hours: \( 185 - 112.50 = 72.50 \) for 5 hours.
- From 10 to 15 hours: \( 257.50 - 185 = 72.50 \) for 5 hours.
- From 15 to 20 hours: \( 330 - 257.50 = 72.50 \) for 5 hours.
It seems the average earning per 5 hours from 5 onwards is \( 72.50/5 = 14.50 \) per hour.
However, instead of assuming this, we can simply observe the trend in the provided data:
- From 0 to 5 hours: $22.50 per hour
- From 5 to 10 hours: $14.50 per hour
- From 10 to 15 hours: $14.50 per hour
- From 15 to 20 hours: $14.00 per hour
We can see the hourly pay decreases, so the easiest way to find out how much Amy will earn at 40 hours is to extrapolate at the same rate taking the last known payment structure.
From the last known payment (20 hours, $330), we can estimate that from 20 to 40 hours, the pay will be $14.00/hour.
Thus:
\[
\text{Earnings from Company 1} = 40 \times 14.00 = 560
\]
**Earnings from Company 2:**
- The pay rate is $12.50 per hour plus an $80 bonus.
\[
\text{Earnings from Company 2} = (40 \times 12.50) + 80 = 500 + 80 = 580
\]
**Now, comparing the two:**
- Earnings from Company 1 = $560
- Earnings from Company 2 = $580
Finally, we calculate the difference:
\[
580 - 560 = 20
\]
Thus, Amy will earn $20 more in Company 2.
So the correct answer is: **C** She will earn $20 more in Company 2.
**Earnings from Company 1:**
From the data given, we can see that the salary increases with hours worked. Since we have data for up to 20 hours, we can observe the pattern or derive the equation.
Let's find the rate per hour in Company 1.
Calculating the change in earnings:
- From 0 to 5 hours: \( 112.50 - 0 = 112.50 \) for 5 hours.
- From 5 to 10 hours: \( 185 - 112.50 = 72.50 \) for 5 hours.
- From 10 to 15 hours: \( 257.50 - 185 = 72.50 \) for 5 hours.
- From 15 to 20 hours: \( 330 - 257.50 = 72.50 \) for 5 hours.
It seems the average earning per 5 hours from 5 onwards is \( 72.50/5 = 14.50 \) per hour.
However, instead of assuming this, we can simply observe the trend in the provided data:
- From 0 to 5 hours: $22.50 per hour
- From 5 to 10 hours: $14.50 per hour
- From 10 to 15 hours: $14.50 per hour
- From 15 to 20 hours: $14.00 per hour
We can see the hourly pay decreases, so the easiest way to find out how much Amy will earn at 40 hours is to extrapolate at the same rate taking the last known payment structure.
From the last known payment (20 hours, $330), we can estimate that from 20 to 40 hours, the pay will be $14.00/hour.
Thus:
\[
\text{Earnings from Company 1} = 40 \times 14.00 = 560
\]
**Earnings from Company 2:**
- The pay rate is $12.50 per hour plus an $80 bonus.
\[
\text{Earnings from Company 2} = (40 \times 12.50) + 80 = 500 + 80 = 580
\]
**Now, comparing the two:**
- Earnings from Company 1 = $560
- Earnings from Company 2 = $580
Finally, we calculate the difference:
\[
580 - 560 = 20
\]
Thus, Amy will earn $20 more in Company 2.
So the correct answer is: **C** She will earn $20 more in Company 2.