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.
A) Yes, his claim is believable. Let represent the number of circular tables, and let r represent the number of rectangular tables. Use his claim to set up a system of equations c+r=9 and 8c+10r=100. The solution of this system is (−5,14).
B) No, his claim is not believable. Let c represent the number of circular tables, and let r represent the number of rectangular tables. Use his claim to set up a system of equations c+r=9 and 8c+10r=100. The solution of this system is (−5,14), but there cannot be a negative number of circular tables.
C) No, his claim is not believable. Let c represent the number of circular tables, and let r represent the number of rectangular tables. Use his claim to set up a system of equations c+r=9 and 10c+8r=100. The solution of this system is (14,−5), but there cannot be a negative number of rectangular tables.
D) Yes, his claim is believable. Let c represent the number of circular tables, and let r represent the number of rectangular tables. Use his claim to set up a system of equations c+r=9 and 10c+8r=100. The solution of this system is (14,−5).