Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences and show your work.
To find out if Tess has enough money to purchase the book, we need to first calculate the discounted selling price.
The book's normal price is $24.50.
We apply a 15% discount: 0.15 * $24.50 = $3.675
We subtract this discount from the normal price: $24.50 - $3.675 = $20.825
Next, we need to calculate the sales tax on the discounted selling price.
The sales tax is 10% of the discounted selling price: 0.10 * $20.825 = $2.0825
Finally, we add the sales tax back to the discounted selling price to find the total purchase amount: $20.825 + $2.0825 = $22.9075
Since Tess and Dan each have $24.00 to spend at the book fair, and the total purchase amount is $22.9075, both Tess and Dan have enough money to purchase the book.
Now let's check if Dan's approach is correct.
Dan takes 85% of the normal purchase price: 0.85 * $24.50 = $20.825
Then, he computes 110% of the reduced price: 1.10 * $20.825 = $22.9075
Dan's approach leads to the same total purchase amount as Tess's approach. Therefore, both Tess and Dan are correct in their calculations.
In conclusion, both Tess and Dan have enough money to purchase the book.