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.