Question

Alfred and Larissa 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, Alfred 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. Larissa takes 65% of the normal purchase price and then computes 110% of the reduced price. Is Alfred correct? Is Larissa correct? Do they have enough money to purchase the book? Explain your answer using complete sentences and show your work.

Answer 1

Answer: See explanation

Explanation:

The normal cost of the book plus the sales tax will be:

= $28.50 + ($28.50 × 10%)

= $28.50 + ($28.50 × 0.1)

= $28.50 + $2.85

= $31.35

Since there's a discount of 35%, the amount they'll have to pay will be:

= $31.35 - ($31.35 × 35%)

= $31.35 - ($31.35 × 0.35)

= $31.35 - $10.9725

= $20.3775

They do not have enough money to make the purchase.

Alfred takes 35% of $28.50 and subtracts that amount from the normal price. Alfred's calculation is shown below:

= $28.50 - (35% of $28.50)

= $28.50 - (0.35 × $28.50)

= $28.50 - $9.975

= $18.525

He takes 10% of the discounted selling price and adds it back to find the purchase amount. This will be:

= $18.525 + (10% × $18.525)

= $18.525 + $1.8525

= $20.3775

Alfred is correct

Larissa takes 65% of the normal purchase price and then computes 110% of the reduced price. This will be:

= 65% × $28.50

= 0.65 × $28.50

= $18.525

= 110% × $18.525

= 1.1 × $18.525

= $20.3775

Larisa is also correct