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 [tex]\$ 250[/tex] plus [tex]\$14[/tex] per hour
Colorful pens charges [tex]\$22[/tex] 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
[tex]\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[/tex]
Now, Let us check charges after 32 hours.
[tex]\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}[/tex]
So, at 31 hours colorful pens are economical but at 32 hours Tim painting is economical.
