1. 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?
Answer: C
The numbers needed to determine how many small balloons were sold are $3, $5, $4000, and 500.
To find out how many small balloons were sold, one needs to know the prices of the small and large balloons ($3 and $5, respectively), the total receipts for small and large balloons ($4000), and the number of large balloons sold (500). These values are essential to set up the equations required to solve for the number of small balloons.
A) $4 and $4000 only
This option is incorrect because it lacks the necessary price of the small balloon ($3) and the number of large balloons sold (500). Knowing just the price of the medium balloon ($4) and the total receipts does not provide enough information to calculate the number of small balloons.
B) $4, $4000, and 500 only
This choice is incorrect since it includes the price of the medium balloon ($4) instead of the price of the small balloon ($3). It also misses the price of the large balloon ($5), which is essential to calculate the total revenue from large balloons.
C) $3, $5, $4000, and 500 only
This option is correct as it includes both balloon prices ($3 for small and $5 for large), the total receipts for small and large balloons ($4000), and the number of large balloons sold (500). All these elements are necessary to solve for the number of small balloons sold.
D) $3, $4, $1600, and $4000 only
This option is incorrect because, while it includes the price of the small balloon ($3), it does not include the price of the large balloon ($5) and the number of large balloons sold (500). Without this information, it would be impossible to accurately determine the number of small balloons.
E) $3, $4, $5, $1600, $4000, and 500
This choice is also correct but includes unnecessary information. While it has all the relevant prices and totals, the key information needed to solve for the small balloons can be derived from option C, which is more concise.
Conclusion
Option C is definitively the best choice because it includes all the necessary information required to solve the problem: the prices of the small and large balloons, the total receipts from the sales of both, and the count of large balloons sold. Other options fail to provide the full set of required data, making them insufficient for solving the question accurately.