In printing an article of 21,000 words, a printer decides to use two sizes of type. Using the larger type, a printed page contains 1,200 works. Using the smaller type type, a page contains 1,500 words. The article is allotted 16 full pages in a magazine. How many pages must be in the larger type?
I think the related questions below will provide the method of solution.
To solve this problem, we can set up a system of equations. Let's denote the number of pages in the larger type as "x", and the number of pages in the smaller type as "y".
From the given information, we know that:
1. The total number of words in the article is 21,000 words.
2. Using the larger type, a printed page contains 1,200 words.
3. Using the smaller type, a page contains 1,500 words.
4. The total number of pages is 16.
Based on the given information, we can write the following equations:
Equation 1: x + y = 16 (since the total number of pages is 16)
Equation 2: 1,200x + 1,500y = 21,000 (since the total number of words in the article is 21,000)
To solve this system of equations, we can either use substitution or elimination method. Let's solve it using the elimination method.
First, we can rewrite Equation 1 as:
x = 16 - y
Now, substitute this value of x into Equation 2:
1,200(16 - y) + 1,500y = 21,000
Simplifying the equation:
19,200 - 1,200y + 1,500y = 21,000
300y = 1,800
Now, solve for y:
y = 1,800 / 300
y = 6
Substitute the value of y back into Equation 1 to find x:
x + 6 = 16
x = 16 - 6
x = 10
Therefore, there must be 10 pages in the larger type.
To find out how many pages must be in the larger type, we need to set up an equation based on the given information.
Let's assume x represents the number of pages in the larger type.
We know that the total number of pages allotted for the article is 16.
So, the number of pages in the smaller type would be (16 - x), as the remaining pages will be in the smaller type.
According to the given information, a page with the larger type contains 1,200 words, and a page with the smaller type contains 1,500 words.
Therefore, the total number of words on the pages with the larger type is (1,200 * x), and the total number of words on the pages with the smaller type is (1,500 * (16 - x)).
Since the total number of words in the article is 21,000, we can set up the equation:
(1,200 * x) + (1,500 * (16 - x)) = 21,000
Now we can solve this equation to find the value of x, which represents the number of pages in the larger type.
By simplifying the equation, we have:
1,200x + 24,000 - 1,500x = 21,000
-300x + 24,000 = 21,000
-300x = 21,000 - 24,000
-300x = -3,000
Dividing both sides by -300, we get:
x = -3,000 / -300
x = 10
Therefore, there must be 10 pages in the larger type.