Question

The table shows prices for newspaper advertising. A store purchased 1/4 pages, 1/2 pages and full pages of page space in equal numbers for a total of $11,500. What is the total amount of page space the store purchased? PRICES FOR NEWSPAPER1/4 pages. $200 1 /2 pages $350 full page. $600

Answer 1

Let n be the amount of pages of each type. Since pages of 1/4, 1/2 and full pages were bought in equal amounts, then the total amount of purchased paper is:

`n*(1)/(4)+n*(1)/(2)+n*1=((1)/(4)+(1)/(2)+1)n`

On the other hand, since each 1/4 page costs $200, each 1/2 page costs $350 and a full page $600, then the total amount of money spent on that is:

`200n+350n+600n=1150n`

The total is also equal to $11,500. Then:

`\begin{gathered} 1150n=11,500 \\ \Rightarrow n=(11,500)/(1150) \\ \Rightarrow n=10 \end{gathered}`

Then, substitute n=10 into the first expression to find the total amount of page space that was purchased:

`((1)/(4)+(1)/(2)+1)*10=(7)/(4)*10=(35)/(2)=17.5`

Therefore, the total amount of space that was purchased was:

`17.5\text{ pages}`