Multiple Choice Question

Question

Jerry makes souvenirs to sell in his shop. For one batch of souvenirs, he spends
dollars for materials and hopes to make
dollars in profit. He writes the inequality
to represent the price,
, in dollars, for each souvenir and the number of souvenirs,
, that he needs to sell to make
dollars in profit. He knows that he can make at most
souvenirs from the materials.

Which statement BEST describes the price Jerry must charge for each souvenir in order to make
dollars in profit?

A.
He must charge at most $
for each souvenir.

B.
He must charge at least $
for each souvenir.

C.
He must charge at most $
for each souvenir.

D.
He must charge at least $3 for each souvenir.

Answer 1

To determine the correct statement regarding the price Jerry must charge for each souvenir in order to make a certain dollar profit, we first need to analyze the inequality that Jerry has written. Generally, the profit he wants to make can be represented by the equation:

\[ \text{Profit} = \text{(Price per souvenir)} \times \text{(Number of souvenirs sold)} - \text{(Cost)} \]

If we set \( p \) as the price per souvenir and \( n \) as the number of souvenirs, then the equation for profit becomes:

\[ p \cdot n - \text{(Cost)} \geq \text{Profit} \]

Rearranging this gives:

\[ p \cdot n \geq \text{Profit} + \text{(Cost)} \]

To ensure that he meets his profit goal, Jerry needs to either charge a certain price that accounts for the total profit goal or be conscious of the maximum amount he can charge depending on how many souvenirs he plans to sell.

Given the multiple-choice answers you've provided, if the inequality results in a requirement that price must meet or exceed a certain amount for a given quantity sold to fulfill the profit condition, the statement should correctly reflect that necessity.

Thus, the answers can be summarized:

• If he must charge at least a certain price to achieve his desired profit, then "B" ("He must charge at least $X for each souvenir") would be appropriate.
• If the maximum he can charge needs to not exceed a certain amount to remain feasible based on his maximum production cap, then "A" or "C" could apply depending on the wording of those options (since both A and C are saying he should charge at most, but have different values).

However, without specified values or context to these statements, it is challenging to deduce the suitable choice definitively.

Since we aim to understand the mechanics of how he can attain his stated profit margin, it is likely the answer that specifies a minimum price, thus:

B. He must charge at least $X for each souvenir.

If a specific price \( 3 \) was provided in context either through another part of your question or your understanding, then it would make sense to lean towards "D" as the choice in this scenario. Otherwise, "B" is generally the appropriate mathematical representation of needing to charge something to meet profit criteria.

In conclusion, please refer to the complete equation or inequality stated for a precise resolution.