# John is writing an article. The article is limited to 48000 words. He decides to use two types of font.Large font is 1800 words per page, small font is 2400 words per page. He is allowed 21 pages...

John is writing an article. The article is limited to 48000 words. He decides to use two types of font.

Large font is 1800 words per page, small font is 2400 words per page. He is allowed 21 pages for this article. How many pages are in small font?

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### 3 Answers

Large font ==> 1800 words / page

Small font ==> 2400 words/ page

Total pages = 21 and 48000 words

Now let us assume that:

x = number of pages with Large Font

y= number of pages with small font

==> x + y = 21 ...............(1)

Number of words are:

Number of words of the large font pages = 1800*x

Number of words of the small font pages = 2400*y

==> Total number of words:

1800x + 2400 y = 48000

==> 18x + 24y = 480

==> 3x + 4y = 80 .............(2)

But from (1) : x = 21 - y

==> 3( 21-y) + 4y = 80

==> 63 - 3y + 4y = 80

==> y= 80 - 63

==>** y= 17**

**==> x = 4**

**Then he needs to write 17 Small font pages and 4 large font pages.**

Let x be the number of pages in small font and y be the number of pages in big font.

So the total pages is 21. Or x+y = 21. So y = 21-x.

So the number of words in small font at the rate of 2400 words per page in x pages = 2400x.

The number of words in big fonts in 21-x pages at the rate of 1800 words per page = 1800 (21-x).

Therefore the total words = 2400x+1800(1-x) which should be 48000 words.

Therefore 2400x+1800(21-x) = 48000

2400x-1800x +21*1800= 48000

(2400-1800)x = 48000 - 21*1800 = (480-21*18)100

600x = (480-378)100

6x = 102

x = 102/6 =17.

So y = 21-x = 21-17 = 4.

So John use 17 pages of small fonts and 4 pages of big font

Let x = number of large font pages.

let y = number of small font pages.

We'll calculate the number of pages written with large fonts:

1 page = 1800 words

2 pages = 2*1800 = 3600 words

x pages = x*1800

We'll calculate the number of pages written with small fonts:

1 page = 2400 words

2 pages = 2*2400 = 4800 words

y pages = 2400y

1800x + 2400y = 48000 (1)

We also know that John is allowed to write 21 pages:

x + y = 21 (2)

x = 21 - y (3)

We'll substitute (3) in (1):

1800(21-y) + 2400y = 48000

We'll remove the brackets:

37800 - 1800y + 2400y = 48000

We'll combine like terms:

600y = 48000 - 37800

600y = 10200

6y = 102

y = 17

x = 21 - y

x = 21 - 17

x = 4

**The pages written with small fonts: y = 17.**