Question

Shirley is going to have the exterior of her home painted. Tim’s painting charges $250 plus $14 per hour. colorful paints charges $22 per hour. How many hours with the job need to take for Tim’s painting to be the better deal?

Answer 1

To determine how many hours would make Tim's painting the better deal, we can set up an equation comparing the total costs of Tim's painting and Colorful Paints.

1. **Tim's Painting Cost**:
The total cost for Tim's painting can be expressed as:
\[
\text{Cost}_\text{Tim} = 250 + 14h
\]
where \( h \) is the number of hours.

2. **Colorful Paints Cost**:
The total cost for Colorful Paints can be expressed as:
\[
\text{Cost}_\text{Colorful} = 22h
\]

3. **Setting Up the Inequality**:
We want to find the values for \( h \) where Tim's painting is cheaper than Colorful Paints. This gives us the inequality:
\[
250 + 14h < 22h
\]

4. **Solving the Inequality**:
- First, we'll subtract \( 14h \) from both sides:
\[
250 < 22h - 14h
\]
Simplifying that, we have:
\[
250 < 8h
\]
- Now, we divide both sides by 8:
\[
\frac{250}{8} < h
\]
Simplifying \( \frac{250}{8} \):
\[
31.25 < h
\]

5. **Conclusion**:
Thus, for Tim's painting to be the better deal, the job would need to take more than 31.25 hours. Since in practice, \( h \) must be a whole number, it means that if the job takes **at least 32 hours**, Tim's painting will be the better deal.

So, if Shirley’s job is projected to take **32 hours or more**, she should go with Tim’s Painting.