(03.01 MC)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.
I think sales tax is calculated after all discounts have been applied.
the cost of the book
= [ discounted price ] + [ sales tax ]
= [ discounted price ] + [ 10% of discounted price ]
= [ 65% of orig price ] + [ 10% of (65% of orig price) ]
= [ 65% * $28.50 ] + [10% * (65% * $28.50) ]
= [ 0.65 * $28.50 ] + [0.10 * (0.65 * $28.50) ]
= [ $18.525 ] + [ 0.10 * ($18.525) ]
= $18.525 + $1.8525
= $20.3775 ≈ $20.38
Alex's method and Lara's method are both correct.
They have enough money to purchase the book.