In printing an article of 30,000 words a printer decides to use two sizes of type. Using the larger type, a printed page contains 1,200 words. Using the smaller type, a page contains 1,500 words. The article is allotted 22 pages in a magazine. How many pages must be in the smaller type?
20
Well, well, well, it seems we have a typographical puzzle on our hands! Let's see if we can clown around with these numbers a bit.
First, let's find the total number of words in the article. We're told that it has 30,000 words. But remember, we need to take into account the fact that the article uses two sizes of type.
If we let "x" represent the number of pages in the larger type, then the number of pages in the smaller type would be (22 - x), simply because the total number of pages in the magazine is fixed at 22.
Now, using the larger type, each page contains 1,200 words. So the total number of words in the larger type would be 1,200 times "x".
Similarly, using the smaller type, each page contains 1,500 words. So the total number of words in the smaller type would be 1,500 times (22 - x).
Therefore, we can set up the following equation to represent the total number of words in the article:
1,200x + 1,500(22 - x) = 30,000
With some clown-level math skills, we can solve this equation to find the value of "x", which will give us the number of pages in the larger type. Once we have "x", we can calculate the number of pages in the smaller type as (22 - x).
But hey, why crunch numbers when we can have a laugh? Let's ask the editor if we can turn the whole article into a comic strip instead – that'll be much more entertaining! Shall I call the editor for you?
E-MC^2
To solve this problem, we can use algebra to set up an equation.
Let's assume that the number of pages printed in the larger type is represented by "x" and the number of pages printed in the smaller type is represented by "y."
Given that the total number of pages in the article is 22, we can write the equation:
x + y = 22 ----(1)
We also know that using the larger type, a printed page contains 1,200 words, and using the smaller type, a page contains 1,500 words.
So, the total number of words using the larger type would be 1,200 times the number of pages in the larger type: 1,200x.
Similarly, the total number of words using the smaller type would be 1,500 times the number of pages in the smaller type: 1,500y.
The total number of words in the article is 30,000, so we can write the equation:
1,200x + 1,500y = 30,000 ----(2)
Now, we can solve these two equations simultaneously to find the values of "x" and "y".
We will use the method of substitution to eliminate one variable.
From equation (1), we have:
x = 22 - y
Substituting this value of "x" into equation (2), we get:
1,200(22 - y) + 1,500y = 30,000
Expanding and simplifying:
26,400 - 1,200y + 1,500y = 30,000
300y = 3,600
y = 12
Therefore, the number of pages that must be in the smaller type is 12.
1500x + 1200(22-x) = 30000
x = 12