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} * 14=\mathrm{h} * 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 * 14 \rightarrow 250+448 \rightarrow \$ 698} \\\\ {\text { His charge at } 31 \text { hours } \rightarrow 698-14 \rightarrow \$ 684} \\\\ {\text { Colorful pens charges } \rightarrow 32 * 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.