Circular and rectangular tables are being set up for a banquet. Each circular table has 8 chairs and each rectangular table has 10 chairs. Suppose 100 chairs are needed for the banquet, and there is no room for any more than that. Is it possible to use exactly 6 circular tables? Explain.
No, it is not possible to use exactly 6 circular tables if 100 chairs are needed for the banquet.
If each circular table has 8 chairs, then 6 circular tables would have a total of 6 x 8 = 48 chairs.
Since the total number of chairs needed is 100, there would still be a shortfall of 100 - 48 = 52 chairs if only circular tables were used.
Therefore, in order to meet the requirement of 100 chairs, some rectangular tables would also need to be used in addition to the circular ones.
how many rectangle chairs would be needed?
To find the number of rectangle chairs needed, we can subtract the number of circular chairs from the total number of chairs needed.
If we assume 6 circular tables with 8 chairs each, this gives us a total of 6 x 8 = 48 circular chairs.
To reach a total of 100 chairs, we would need 100 - 48 = 52 rectangle chairs.
Therefore, 52 rectangle chairs would be needed in addition to the 48 circular chairs to meet the requirement of 100 chairs.
To determine whether it is possible to use exactly 6 circular tables, we need to calculate the total number of chairs that would be available with 6 circular tables.
Since each circular table has 8 chairs, the total number of chairs with 6 circular tables would be: 6 tables x 8 chairs per table = 48 chairs.
However, we need 100 chairs for the banquet, which is more than what can be provided by the 6 circular tables. Therefore, it is not possible to use exactly 6 circular tables for the banquet.
To solve this problem, we can explore other combinations of circular and rectangular tables to find a solution that meets the requirement of having exactly 100 chairs.