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. Be sure to show your calculations for determining the final cost of the book for each student.

Answer 1

the book fair has a 35% discount. after the discount is applied there is also a 10% sales tax.

they both want to buy a book that costs 28.50 + 10% tax. they both have 21 dollars and they want to know if they have enough.

Answer 2

Alex is trying to calculate the final price of the $28.50 book by:

1. calculating 35% of 28.50
2. subtracting 35% of 28.50 from 28.50 to find the discounted price
3. calculating 10% of the discounted price
4. adding on that 10% back to the discounted price to find the sales tax

Answer 3

if we want to represent this mathematically

amount taken off the total: 35% of 28.50 = 0.35 * 28.50

discounted price = (28.50 - 0.35 * 28.50)

10% of the discounted price: 0.10 * (28.50 - 0.35 * 28.50)

10% added back to the discounted price:

(28.50 - 0.35 * 28.50) + 0.10 * (28.50 - 0.35 * 28.50) = the final amount Alex pays

Answer 4

let me give you some time to process this information, it's a lot to take in

Answer 5

with that being said

do you think Alex's steps are a valid way to calculate the final price? or did he make a mistake somewhere?

Answer 6

@caira12 still there?

Answer 7

they both will spend $20.38 at the book fair because 35% of $28.50 is $18.53 which is the books price but then you have to add tax when you add tax 10% of $18.53 is $1.85 then add up that with the price of the book and you get $20.38

Answer 8

Alex is correct. they have enough to purchase the book!

Answer 9

thank you sm! Sorry im responding so late i had a huge storm and everything shut down.