Question

A customer brings 8 pencils to the cashier.The cashier suggests that the total cost to purchase 10 pencils would be less expensive.State whether the cashier is correct or incorrect.Justify your answer.

Answer 1

The cashier is correct. Purchasing 10 pencils would likely result in a lower cost per pencil, assuming a bulk discount or special pricing for larger quantities.

Step-by-step explanation:

The concept behind the cashier's suggestion lies in the potential application of bulk pricing or discounts for larger quantities. It is common for sellers to offer a reduced unit cost when customers purchase items in greater quantities.

To justify this, let's assume the cost of each pencil is
`\(C\)` dollars. If the customer brings 8 pencils, the total cost
`(\(TC_8\)) would be \(8C\).` Now, if the customer were to buy 10 pencils, the total cost
`(\(TC_(10)\))` could be reduced if there's a bulk discount, making each pencil potentially less expensive.

To illustrate, if the total cost for 8 pencils is
`\(8C\)`, and the total cost for 10 pencils is
`\(TC_(10)\),` the cashier's suggestion holds if
`\(TC_(10) < 8C\).` This implies that the average cost per pencil when buying 10 should be less than the cost per pencil when buying 8.

However, for a comprehensive assessment, it's crucial to have specific information on the pricing structure or any applicable discounts. Without this information, the analysis remains based on general assumptions about bulk pricing, and the conclusion may vary based on the actual pricing policy of the seller.