SOLUTION: In laying out an article of 32,000 words, an editor decides to use two sizes of type. Using the larger type, a printed page contains 900 words. Using the smaller type, a page conta

Question 1044585: In laying out an article of 32,000 words, an editor decides to use two sizes of type. Using the larger type, a printed page contains 900 words. Using the smaller type, a page contains 1,400 words. The article is allotted 30 full pages in a magazine. How many pages must be in the small type?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
article contains 32000 words.
with larger type page contains 900 words.
with smaller type a page contains 1400 words.
the article is allotted 30 full pages.
how many pages must be in small type.

let x = the number of pages in small type.
let y = the number of pages in large type.

900*x + 1400*y = 32000

this means that the number of pages with 900 words on them times 900 plus the number of pages with 1400 words on them times 1400 must be equal to 32000 words.

x + y = 30

this means that the total number of pages must be equal to 30.

these are 2 equations that need to be solved simultaneously.

this means that the same solution for x and y applies to both equations.

start with:

900x + 1400y = 32000
x + y = 30

multiply both sides of the second equation by 900 and leave the first equation as is to get:

900x + 1400y = 32000
900x + 900y = 27000

subtract the second equation from the first to get:

500y = 5000

solve for y to get y = 5000/500 = 10

since x + y = 30, then x must be equal to 20.

your solution should be that the number of pages in small type needs to be 10 while the number of pages in large type needs to be 20.

to see if this is correct, replace x with 20 and y with 10 in the original equations to see if they hold true.

the original equations are:

900x + 1400y = 32000
x + y = 30

x = 20 and y = 10

x + y = 30 becomes 30 = 30 which is true.

900x + 1400y = 32000 becomes 18000 + 14000 which is equal to 32000 which makes the first equation true as well.

your solution is that the number of pages that must be in small type is 10.

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