Find the number of pages each size fonts will be printed on.

Question

Jacob needs to print a document with a total of 12,600 words on exactly 12 pages. In large font, 850 words can fit on one page and in small font, 1,150 words can fit on one page. Find the number of pages in the document that should be printed in small font and the number of pages that should be printed in large font.

Answer 1

Hi Jacob,

 

Since 850 words can fit on a page in large font, a word takes up about 1/850 of a page in large font.

 

Since 1150 words can fit on a page in small font, a word takes up about 1/1150 of a page in small font.

  

Let n be the number of words in small font. Then, 12,600 - n are the number of words in large font.

 

The number of pages = number of pages in small font + number of pages in large font

 

or

 

12 = n(1/1150 page)+ (12600 - n)(1/850 page)

 

Let's multiply this equation through by 50.

 

(12)(50) = (50)n/1150 + (12600 - n)(50)/850

 

or

 

600 = n/23 + (12600 - n)/17

 

Now, 23*17 = 391

 

Let's multiply both sides of the last equation by 391.

 

(391)(600) = 17n + (12600 - n)(23)

 

or

 

234,600 = 17n + 289,800 - 23n

 

or 6n = 55,200

 

or

 

n = 9,200 words in small font.

 

So, there are 12,600 - n = 12,600 - 9,200 = 3,400 words in large font.

 

Check:

 

(9200 words small font)(1/1150 page) + (3,400 words large font)(1/850 page) = 8 pages small + 4 pages large = 12 pages