Question

Oscar and Kim have $22.00 each to spend at a book fair, where all students receive a 30% 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, Oscar takes 30% 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. Kim takes 70% of the normal purchase price and then computes 110% of the reduced price. Is Oscar correct? Is Kim correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.

Answer 1

Oscars work is the correct way to check, but they do not have enough money because when you take the 30% discount and subtract you get 21.90, and when you take and find the 10% sales tax and add it back you get 24.10, which is 2.10 over their budget, so in conclusion they do not have enough money to purchase the book, and Oscars work was the correct way to find out if they had enough money.

Answer 2

The book normally sells for 28.50 + 10% sales tax

Oscar :
28.50 - 0.30(28.50) = 28.50 - 8.55 = 19.95
0.10(19.95) + 19.95 = 2 + 19.95 = 21.95

Kim :
0.7(28.50) = 19.95
1.10(19.95) = 21.95

Both Oscar and Kim are correct. Taking 30% off is the same as paying 70%. Taking 10% of the sales price and adding it back to the sale price is the same as taking 110% of the sale price. Both Oscar and Kim will have enough to purchase the book.