Tayla purchased a large box of comic books for $300. She gave 15 of the comic books to her brother and then sold the rest on an internet website for $330, making a profit of $1.50 on each one. How many comic books were in the box? What was the original price of each comic book?
Let x denote the number of comic books in the box. Her cost per magazine was 300/x. If she gave 15 to her brother, then she sold (x-15) magazines on the internet site. The price she got per magazine was 330/(x-15). This was $1.50 more than her cost per magazine. So
330/(x-15) - 300/x = 1.5
Multiply both sides by x(x-15):
330x - 300(x-15)) = 1.5x(x-15)
330x - 300x + 4500 = 1.5x² - 22.5x
30x + 4500 = 1.5x² - 22.5x
Divide both sides by 1.5 (I like integers)
20x + 3000 = x² - 15x
0 = x² - 35x - 3000
Using the quadratic formula,
x = [35 ± √(1225 + 12000)]/2
x = 75 or x = -40
We must reject the negative solution of course.
The original price of the comic books, per book, was $300/75 = $4
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Let x denote the number of comic books in the box. Her cost per magazine was 300/x. If she gave 15 to her brother, then she sold (x-15) magazines on the internet site. The price she got per magazine was 330/(x-15). This was $1.50 more than her cost per magazine. So
330/(x-15) - 300/x = 1.5
Multiply both sides by x(x-15):
330x - 300(x-15)) = 1.5x(x-15)
330x - 300x + 4500 = 1.5x² - 22.5x
30x + 4500 = 1.5x² - 22.5x
Divide both sides by 1.5 (I like integers)
20x + 3000 = x² - 15x
0 = x² - 35x - 3000
Using the quadratic formula,
x = [35 ± √(1225 + 12000)]/2
x = 75 or x = -40
We must reject the negative solution of course.
The original price of the comic books, per book, was $300/75 = $4
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