To determine if Ryan's claim is believable, we need to calculate the total number of chairs that 9 tables can accommodate.
Let's assume there are x circular tables and y rectangular tables.
For circular tables, each table has 8 chairs, so the total number of chairs from circular tables is 8x.
For rectangular tables, each table has 10 chairs, so the total number of chairs from rectangular tables is 10y.
According to Ryan's claim, the total number of chairs is 100, so we have the equation:
8x + 10y = 100
Now, let's try to find integer solutions for x and y.
Looking at this equation, we can see that for every 2 circular tables added, we need 5 rectangular tables to maintain a total of 100 chairs.
If we test some possible values, we see that when x = 0 and y = 10 (i.e. 10 rectangular tables), the equation holds true:
8(0) + 10(10) = 0 + 100 = 100.
So, one possible solution is 10 rectangular tables and 0 circular tables.
This means that Ryan's claim is not believable because he claims to have used 9 tables to set up 100 chairs, but we have found a solution using 10 tables.
Circular and rectangular tables are set up for a banquet. Each circular table has 8
chairs and each rectangular table has 10
chairs. Ryan claims that he used 9
tables to set up 100
chairs for the banquet. Is his claim believable? Explain.
1 answer