Question

alex and Lara have $21.00 each to spend at a book fair, where all students receive a 35% discount. They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax. To check if he has enough to purchase the book, Alex takes 35% of $28.50 and subtracts that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount. Lara takes 65% of the normal purchase price and then computes 110% of the reduced price. Is Alex correct? Is Lara correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.

Answer 1

Both Alex and Lara correctly calculated the final price of the book, which is $20.3775 after a 35% discount and a 10% sales tax. Therefore, they each have enough money to purchase the book since they have $21.00 each.

Step-by-step explanation:

Alex and Lara want to check if they each have enough money to purchase a book that has a normal price of $28.50 with a student discount and sales tax applied. We need to calculate the final price both students will pay to determine if they can afford the book with their $21.00 each.

Alex's method: First, he calculates the discount by taking 35% off the normal price:

• $28.50 × 0.35 = $9.975

He then subtracts the discount from the normal price:

• $28.50 - $9.975 = $18.525

He adds the 10% sales tax to the discounted price:

• $18.525 × 1.10 = $20.3775

Lara's method: She calculates the price after the discount by taking 65% of the normal price:

• $28.50 × 0.65 = $18.525

Then, she calculates 110% of this reduced price to include the sales tax:

• $18.525 × 1.10 = $20.3775

Both Alex and Lara are correct in their computations, and the final price they both arrive at is $20.3775. This means they each have enough money since both have $21.00 and the book costs less than that after discounts and tax are applied.

Answer 2

Alex is correct the book would cost $18.52 before taxes adding 10% tax the book would cost an additional $1.85 for a total of $20.37. This would be just under the $21.00 that both Alex and Laura had to spend. Laura tried to combined the 35% discount which you cannot do. So yes they both would be able to purchase the book.