Question

[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 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 than if the profits were divided in proportion to the amount invested?] / {Can you clearly give me the details about above two questions, please? Thanks}

Answer 1

Qns. 1 [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 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?]

Let x be the number of pages with the larger font size and y be the number of pages with the smaller font size.

Form 2 equations relating both x and y to each other.

x + y = 21 - (1)

1800 x + 2400y = 48000 - (2)

From (1), (multiply by 1800)
1800 x + 1800 y = 37800 - (3)

Take (2) subtract (3)

1800 x + 2400 y - 1800x - 1800 y = 48000 - 37800
600 y = 10200
y= 17

Substitute y = 17 to (1)
x+ 17 = 21
x = 4

4 large pages and 21 smaller pages.

Qns 2. [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 than if the profits were divided in proportion to the amount invested?]

X's profits when divided equally,
4800 /3 = 1600

X's profits when divided based on proportion invested,
\[4800 \times \frac{9000}{9000+4000+ 7000}\]
=2160.

How much less does X receive?
2160 - 1600 = 560 dollars.