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.

See explanation

Step-by-step 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

they would have to work 32 hours.