Mabel bought some notepads for $56. If she was given a discount of 30%, she would be able to buy 40 notepads more. What was the original price of each notepad?
I don't quite understand. When she bought the notepads at $56, was the 30% discount already applied?
I have a feeling James meant to say:
"Mabel bought some notepads for $56. If she had been given a discount of 30% , she would be able to buy 40 notepads more.
Let the original price be x
Number of notepads bought when paying $56 = 56/x
discounted price = .7x
Number of notepads bought at discounted price = 56/(.7x)
56/.7x - 56/x = 40
multiply each term by .7x
56 - 39.2 = 28x
x = .60
the original cost of a notebook was 60 cents.
check: at original price she bought 56/.60 = 93.333..
discounted price = .7(.60) = .42
number bought at .42 = 56/.42 = 133.333 , which is 40 more
mathematically, it checks out, but in reality, how could she have bought
93 1/3 notebooks ?
Poorly thought out question.
To find the original price of each notepad, let's first calculate the discount amount that Mabel received.
Discount amount = 30% of the original price
Discount amount = 30/100 * (original price)
We know that Mabel was able to buy 40 more notepads with the discount, so we can set up an equation:
40 * (original price) = discount amount
Now let's calculate the discount amount:
Discount amount = 30/100 * (original price)
Discount amount = 0.3 * (original price)
Substituting the discount amount into the equation:
40 * (original price) = 0.3 * (original price)
Divide both sides of the equation by the original price:
40 = 0.3
Now, we can solve for the original price:
original price = 40 / 0.3
original price ≈ $133.33
Therefore, the original price of each notepad was approximately $133.33.