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? ___________
Three individuals form a partnership and agree to divide the profits equally. X invests
$9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less
does x receive compared to having the profits divided in proportion to the amounts
invested by X, Y, and Z?
S+L=21
S*2400 + L*1800=48000
Is that correct?
Assuming that their profit sharing should be in the same ratio as their investments
X:Y:Z = 9000:7000:4000
= 9:7:4
= 9x:7x:4x
then 9x+7x+4x = 4800
solve for x, and take it from there.
To find the number of pages that must be in smaller type, we can use the given information. Let's assume the number of pages in larger type is represented as L and the number of pages in smaller type is represented as S.
We know that a page in larger type contains 1,800 words, so the total number of words in the larger type is 1,800L.
Similarly, a page in smaller type contains 2,400 words, so the total number of words in the smaller type is 2,400S.
The article is allotted 21 full pages in the magazine, so we can write the equation:
L + S = 21
We also know that the total number of words in the article is 48,000, so we can write another equation:
1,800L + 2,400S = 48,000
Now we have a system of two equations with two variables. We can solve these equations to find the values of L and S.
First, let's multiply the first equation by 1,800 to eliminate L:
1,800L + 1,800S = 37,800
Subtracting this equation from the second equation gives us:
1,800L + 2,400S - (1,800L + 1,800S) = 48,000 - 37,800
600S = 10,200
S = 10,200 / 600
S = 17
Therefore, the number of pages that must be in smaller type is 17.
To answer the first question, we need to find out how many pages in smaller type are required to print the article. We already know that a page in larger type contains 1,800 words, and a page in smaller type contains 2,400 words.
Let's assume that the number of pages in smaller type is represented by 'x'. The number of pages in larger type would then be '21 - x'.
To calculate the total number of words in the article using larger type, we multiply the number of pages in larger type by the number of words per page in larger type:
Total words in larger type = (21 - x) * 1800
Similarly, the total number of words in the article using smaller type can be calculated:
Total words in smaller type = x * 2400
Since the article contains a total of 48,000 words, we can set up the equation:
Total words in larger type + Total words in smaller type = 48,000
(21 - x) * 1800 + x * 2400 = 48,000
Now we can solve this equation to find the value of 'x', which represents the number of pages in smaller type.