Question

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

Answer 1

It takes 32 hours for Tim’s painting to be better deal.

SOLUTION:

Given, Shirley is going to have the exterior of her home painted  

Tim’s painting charges $\ 250$ plus $\ 14$ per hour  

Colorful pens charges $\ 22$ per hour  

We have to find required hours for Tim’s painting to be the better deal . Let the number hours be h.  So, Tim’s charges = colorful pens charges  

$\rightarrow 250+\mathrm{h} \times 14=\mathrm{h} \times 22 \rightarrow 14 \mathrm{h}+250=22 \mathrm{h} \rightarrow 22 \mathrm{h}-14 \mathrm{h}=250 \rightarrow 8 \mathrm{h}=250 \rightarrow \mathrm{h}=31.25$

Now, Let us check charges after 32 hours.

$\begin{array}{l}{\text { Tim charges } \rightarrow 250+32 \times 14 \rightarrow 250+448 \rightarrow \ 698} \\\\ {\text { His charge at } 31 \text { hours } \rightarrow 698-14 \rightarrow \ 684} \\\\ {\text { Colorful pens charges } \rightarrow 32 \times 22 \rightarrow 704} \\\\ {\text { His charge at } 31 \text { hours } \rightarrow 704-22 \rightarrow \ 682}\end{array}$

So, at 31 hours colorful pens are economical but at 32 hours Tim painting is economical.