SOLUTION: A student plans to spend ¢200 on p notebooks. But the price of the notebooks had increased by ¢10. As a result, the number of notebooks the student could buy was reduced by 1. Find

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Question 1120967: A student plans to spend ¢200 on p notebooks. But the price of the notebooks had increased by ¢10. As a result, the number of notebooks the student could buy was reduced by 1. Find the price of each notebook before the increase.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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Just solved for you under this link

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1120966.html

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1120966.html



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
student plans to spend 200 on p notebooks.
if the price goes up by 10, the student can buy p - 1 notebooks.

let x = the price of one notebook.

you have two equations that need to be solved simultaneously.

they are:

x * p = 200
(x+10) * (p-1) = 200

solve for x in the first equation to get x = 200/p

replace x in the second equation by 200/p to get:

(x+10) * (p-1) = 200 becomes:

(200/p + 10) * (p-1) = 200

multiply both sides of this equation by p to get:

p * (200/p + 10) * (p-1) = 200 * p

since p * (200/p + 10) is equal to 200 + 10p, the equation becomes:

(200 + 10p) * (p-1) = 200p

simplify to get:

200p - 200 + 10p * p - 10p = 200p

the 200p in both sides of the equation cancels out and you are left with:

-200 + 10p^2 - 10p = 0

rearrange the terms in descending order of degree to get:

10p^2 - 10p - 200 = 0

divide both sides of the equation by 10 to get:

p^2 - p - 20 = 0

factor this quadratic equation to get:

(p-5)*(p+4) = 0

solve for p to get p = 5 or p = -4

your solution is p = 5.

when p = 5, x * p = 200 becomes x * 5 = 200 which makes x = 40

when p = 4, x * p = 200 becomes x * 4 = 200 which makes x = 50

x is the price of each notebook.

when the price is 40, you can buy 200 / 40 = 5 notebooks.

when the price is raised by 10 to be equal to 50, you can buy 200 / 50 = 4 notebooks which is 1 less than when the price was 40.

your solution is that the price of each notebook was 40 before the increase.