How do I figure this word problem out?

Printing an article of 48000 words, using two sizes of type. The larger type contains 1800 words per page, the smaller type contains 2400 words.  The article is allowed 21 full pages. How many pages must be in the smaller type?
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1 Answer

How do I figure this word problem out?

Printing an article of 48000 words, using two sizes of type. The larger type contains 1800 words per page, the smaller type contains 2400 words.  The article is allowed 21 full pages. How many pages must be in the smaller type?
 
Large Type = L =1800 L
Small Type = S = 2400S
 
1800S+ 2400L = 48000 <= eq1
L + S = 21
L = 21 - S <= eq2
 
1800 / (12 - S)+ 2400 / S = 48000 / (L+S)
1800S + 2400 L  = 48000
18S + 24L = 480
from eq2
18S + 24(21-S) = 480
 
18S + 24(12) - 24S)  = 480

- 6S + 504 = 480

6S = -(480 - 504)

6S = 24

Small Type (S) = 4 ◄ Ans
 
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