Question

The table shows how the cost of a tractor repair depends on the time needed for the repair.

TRACTOR REPAIR COSTS
Repair Time

(hours)

Cost

(dollars)

2 180
5 450
? 630
10 900
20 1,800
Which expression can be used to find the number that is missing from the third row of the table?

Answer 1

To find the missing repair time corresponding to the cost of $630, we first observe the relationship between the repair time and cost in the table.

From the table, we can see:

- For 2 hours, the cost is $180.
- For 5 hours, the cost is $450.
- For 10 hours, the cost is $900.
- For 20 hours, the cost is $1,800.

Now we can look for a consistent pattern. Let's calculate the cost per hour for the known values:

- For 2 hours:
\[
\frac{180}{2} = 90 \text{ dollars per hour}
\]

- For 5 hours:
\[
\frac{450}{5} = 90 \text{ dollars per hour}
\]

- For 10 hours:
\[
\frac{900}{10} = 90 \text{ dollars per hour}
\]

- For 20 hours:
\[
\frac{1800}{20} = 90 \text{ dollars per hour}
\]

The cost appears to increase linearly at a rate of $90 per hour.

Since we are looking for the repair time corresponding to a cost of $630, we can set up the following equation based on the cost per hour:

\[
\text{Cost} = \text{Repair Time (hours)} \times 90
\]

Substituting the cost of $630 into the equation:

\[
630 = \text{Repair Time} \times 90
\]

Now we can solve for the repair time:

\[
\text{Repair Time} = \frac{630}{90}
\]

Calculating that gives us:

\[
\text{Repair Time} = 7
\]

Thus, the missing number in the third row of the table is 7 hours.

Therefore, the expression that can be used to find the missing number is:

\[
\text{Repair Time} = \frac{630}{90}
\]