In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the larger type, a printed page contains 1,800 words. Using a smaller type, a page contains 2,400 words. The article is allotted 21 full pages in a magazine. How many pages must be in smaller type?

small print pages : x

large print pages : 21-x

2400x + 1800(21-x) = 48000

solve for x

17 pages

To find the number of pages that must be in the smaller type, we need to determine how many words can fit on a page using the smaller type and then calculate how many pages would be needed to print the remaining words.

First, let's calculate the number of words that can fit on a page using the larger type:

Page capacity with large type = 1,800 words

Next, we can calculate the number of words that can fit on a page using the smaller type:

Page capacity with small type = 2,400 words

Now, let's calculate the total number of words that can fit on 21 pages using the larger type:

Total words with large type = Page capacity with large type × Number of pages
= 1,800 words/page × 21 pages
= 37,800 words

To find the number of pages that must be in the smaller type, we need to subtract the total number of words with the larger type from the total number of words in the article:

Remaining words = Total words in the article - Total words with large type
= 48,000 words - 37,800 words
= 10,200 words

Finally, we can calculate the number of pages that must be in the smaller type:

Number of pages with small type = Remaining words / Page capacity with small type
= 10,200 words / 2,400 words/page
= 4.25 pages

Since we can't have fractional pages, we round up to the nearest whole number.

Therefore, we would need 5 pages in smaller type to print the remaining words.

To find out how many pages must be in smaller type, we can set up a system of equations.

Let's assume the number of pages printed in larger type is x, and the number of pages in smaller type is y.

Given:
The larger type contains 1,800 words per page.
The smaller type contains 2,400 words per page.
The total number of pages in the magazine is 21.

We can set up the following equations:

Equation 1: x + y = 21 (since the total number of pages is 21)
Equation 2: 1,800x + 2,400y = 48,000 (since the total number of words in the article is 48,000)

Now, we can solve this system of equations.

First, we'll solve Equation 1 for x:
x = 21 - y

Next, we'll substitute this value of x into Equation 2:
1,800(21 - y) + 2,400y = 48,000

Simplifying the equation, we get:
37,800 - 1,800y + 2,400y = 48,000

Combining like terms:
600y = 10,200

Dividing both sides by 600:
y = 17

Therefore, the number of pages that must be in smaller type is 17.