Question

During a sale at a bookstore, Joseph buys a book at full price. He is given a 50 percent discount on a second book of equal or less value. If Joseph buys two books with a full price of $15 and $10 respectively, by what percent is the total cost of the two books reduced during the sale?

Answer 1

During the sale, the total cost of the two books is reduced by 20%. This is calculated by obtaining the sale price for the second book at a 50% discount and comparing the reduced total cost to the original total cost.

Step-by-step explanation:

The question asks us to calculate the reduction in the total cost of two books during a bookstore sale where the second book is offered at a 50 percent discount if it is of equal or less value than the first book.

Joseph buys one book at $15 and a second book at $10. Without the sale, the total cost would be $15 + $10 = $25. During the sale, he gets the second book at a 50% discount, so he pays $10 / 2 = $5 for it. Thus, the total sale price is $15 (full price of the first book) + $5 (discounted price of the second book) = $20. To find the percent reduction, we compare the sale total to the original total price.

Reduction in total cost = Original total cost - Sale total cost
Reduction in total cost = $25 - $20 = $5

The percent reduction is calculated by dividing the reduction in cost by the original total cost and multiplying by 100.
Percent Reduction = ($5 / $25) × 100 = 20%

Answer 2

Joseph bought a book at full price for $15, then on the sale he got the second one for half price, but we know the second one was $10, and we know that's half the regular price, so the regular price must be twice as much of that, namely $20.

Joseph ended up paying only $25 for both, including the discount on the second, however if there wasn't any sale, he would have paid full price for both, namely 15 + 20, or 35.

so, he didn't pay $35, he paid $25, he saved 10 bucks.

if we take 35 to be the 100%, what is 10 off of it in percentage?


`\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 35&100\\ 10&p \end{array}\implies \cfrac{35}{10}=\cfrac{100}{p}\implies p=\cfrac{10\cdot 100}{35}`