Article of48000words,printer uses2sizes of type.large type,a page has1800words.small type,a page contains2400words.allotted21full pages.How many p in small type

Question

This is a practice quiz. I know the correct answer is 17, but I need to know how to do the problem. Please help! I had to shorten it to fit. Hopefully it makes sense!

Answer 1

Let L = the number of pages with large type

Let S = the number of pages with small type

 

We have two unknowns, L and S, so we need two equations to solve for them.

 

Equation 1 -  Article of 48000 words: (1800)*L + (2400)*S = 48,000

 

1800*L = the number of words on all of the large-type pages

2400*S = the number of words on all of the small-type pages

 

Equation 2 - Allotted 21 full pages: L + S = 21

 

Subtract S from both sides

L = 21 - S

 

Now substitute 21-S in place of L in equation 1. 

 

1800*L + 2400*S = 48,000               [Equation 1]

 

1800*(21-S) + 2400*S = 48,000       [Substituted 21-S in place of L]

 

37,800 - 1800*S + 2400*S = 48,000  

 

Solve for S