At a carnival the price of a small balloon was $3, the price of a medium balloon was $4, and the price of a large balloon was $5. Total receipts for medium balloons were $1600 and total receipts for small and large balloons were $4000. The number of large balloons sold was 500. How many small balloons were sold? To answer the question above, which of the following numbers are needed?

Rationale

$3, $5, $4000, and 500 only.

To determine how many small balloons were sold, we need the prices of small and large balloons, the total receipts for small and large balloons, and the number of large balloons sold. These variables allow us to set up equations to solve for the unknown quantity of small balloons.

A ($4 and $4000 only) YOUR ANSWER

This choice only includes the price of medium balloons and the total receipts for small and large balloons. Without the prices of small and large balloons or the number of large balloons sold, it is impossible to determine how many small balloons were sold.

B ($4, $4000, and 500 only) YOUR ANSWER

While this choice includes the price of medium balloons, the total receipts for small and large balloons, and the number of large balloons, it lacks the price of the small balloon. Without knowing how much the small balloon costs, we cannot calculate the number sold.

C ($3, $5, $4000, and 500 only) CORRECT

This option provides the prices of small and large balloons, the total receipts for small and large balloons, and the number of large balloons sold. With this information, we can create equations to find the number of small balloons sold, making this the correct choice.

D ($3, $4, $1600, and $4000 only) YOUR ANSWER

Although this choice includes the price of small balloons and the total receipts for small and large balloons, it includes the receipts for medium balloons instead of the number of large balloons sold. This information is insufficient to solve the problem.

E ($3, $4, $5, $1600, $4000, and 500) YOUR ANSWER

While this option contains all necessary information, it is not necessary to have the total receipts for medium balloons ($1600) to calculate the number of small balloons sold. Including unnecessary data does not affect the solution, but it is not the most efficient choice.

Conclusion

To solve the problem of how many small balloons were sold, we require the prices of both small and large balloons ($3 and $5), the total receipts for small and large balloons ($4000), and the number of large balloons sold (500). This information allows us to set up the necessary equations and find the unknown quantity of small balloons sold. Thus, the most relevant and sufficient data is captured in option C.

$3, $5, $4000, and 500 only.

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