Chapter 2.4, Problem 10P

Write and solve an equation for each situation. Check your solution.

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 would the job need to take for Tim’s Painting to be the better deal?

To determine

The hours of job needed to take for T’s painting to be the better deal.

Answer to Problem 10P

32 hours.

Explanation of Solution

Given information :

T,s paintng charges $250 plus $14 per hour.

Colorful Paints charges $22 per hour.

Let the hours worked be $x$ .

Hence the total price of Tim’s Painting is $250+14x$ .

The total price of Colorful paints is $22x$ .

First we shall calculate the hours at which both the paints cost the same.

Now we shall equate both equations for total price. We get,

  $\begin{array}{l}250+14x=22x\\ 22x-14x=250\\ 8x=250\\ x=31.25\end{array}$

Therefore we can observe that the price is same for both working for 31.25 hours.

Working more than 31.25, T’s Painting would be a better deal.

Hence it would take 32 hours (next whole number to 31.25) for T’s painting to be the better deal.