Mrs. Goode, the English teacher, assigned a paper. She requires 4,207 words for 6 pages. If Jasper writes 29,449 words, how many pages can he expect to write?

I understand that to write #6# pages you need #4,207# words.
If Jasper writes #29,449# words you have that:
#(29,449)/(4,207)=7# sets of #6# pages or:
#7*6=42# pages

It is a matter of ratio

There are two ways of expressing ratio. One method is to show them in the same format as a digital clock with the colon between

For example 2:3

This does not lend itself to mathematical manipulation as much as #2/3# would

Using method 2:

Target #-> ("6 pages")/(4207 "words")........................(1)#

It is much easier if you use the numerator to represent the 'unit' you are trying to solve for. In this case the unit is "pages".

Let the number of pages needed by Jasper be #x#
The number of words he expects to write is 29449

So to maintain the same ratio of pages to words as the target you write:

#6/4207 = x/29449#

Multiply both sides by 29449 and you have

#(6xx29449)/(4207) =x/1#

so #x = 42# which confirms Geo's solution, as I would expect it to!

This does not reflect a real wold assignment as you usually have a restriction imposed on the number of pages you may submit!