To determine how many hours it would take to repair a tractor at a cost of $630, we can analyze the costs given in the table.
From the information presented:
- 2 hours = $180
- 5 hours = $450
- Unknown hours = $630
- 10 hours = $900
- 20 hours = $1,800
We can observe the increase in cost with the increase in hours:
- From 2 hours to 5 hours, the cost increases from $180 to $450. This is a difference of $270 for 3 hours (5 - 2).
- From 5 hours to 10 hours, the cost increases from $450 to $900. This is a difference of $450 for 5 hours (10 - 5).
- From 10 hours to 20 hours, the cost increases from $900 to $1,800. This is a difference of $900 for 10 hours (20 - 10).
Now, let's specifically look at the cost of $630. This amount falls between the costs of 5 hours ($450) and 10 hours ($900). We can use a proportion to estimate the hours:
Calculating the differences:
- Cost difference from $450 (5 hours) to $630 = $630 - $450 = $180
- Cost per hour from 5 hours to 10 hours can be calculated:
From the previous increase descriptions, we note that:
- From 5 hours to 10 hours ($450 to $900), the cost increased by $450 for 5 hours, which means there is an average cost of $90 per hour (450/5).
Now you can estimate how many additional hours it takes to reach $630:
From $450 for 5 hours, if $90 is charged per hour,
\[ \text{Additional cost from 450 to 630} = 630 - 450 = 180 \]
\[ \text{Additional hours} = \frac{180}{90} = 2 \text{ additional hours} \]
Thus, you would add this to the 5 hours:
\[ 5 + 2 = 7 \text{ hours} \]
Therefore, the number of hours it would take to repair a tractor at a cost of $630 is B. 7.
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