In one restaurant, the round table can seat 10 diners and the rectangular table can seat 4 diners. During the buffet, all the tables in the restaurant were occupied. The number of each type of tables in the restaurant is more than 8 and less than 14. If there were 164 diners, find
(a) the number of rectangular tables
(b) the number of round tables
Rectangular tables |
Number of diners around rectangular tables |
Round tables |
Number of diners around round tables |
Total number of diners |
9 |
9 x 4 = 36 |
9 |
9 x 10 = 90 |
36 + 90 = 126 (x) |
10 |
10 x 4 = 40 |
11 |
11 x 10 = 110 |
40 + 110 = 150 (x) |
11 |
11 x 4 = 44 |
12 |
12 x 10 = 120 |
44 + 120 = 164 (✓) |
(a)
Number of rectangular tables = 11
(b)
Number of round tables = 12
Answer(s): (a) 11; (b) 12