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(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.

Guest May 9, 2017
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 #1
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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.

hectictar  May 9, 2017
edited by hectictar  May 9, 2017
edited by hectictar  May 9, 2017

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