In one canteen, the oval table can seat 7 diners and the round table can seat 4 diners. During the buffet, all the tables in the canteen were occupied. The number of each type of tables in the canteen is more than 6 and less than 13. If there were 117 diners, find
(a) the number of round tables
(b) the number of oval tables
Round tables |
Number of diners around round tables |
Oval tables |
Number of diners around oval tables |
Total number of diners |
7 |
7 x 4 = 28 |
7 |
7 x 7 = 49 |
28 + 49 = 77 (x) |
9 |
9 x 4 = 36 |
10 |
10 x 7 = 70 |
36 + 70 = 106 (x) |
10 |
10 x 4 = 40 |
11 |
11 x 7 = 77 |
40 + 77 = 117 (✓) |
(a)
Number of round tables = 10
(b)
Number of oval tables = 11
Answer(s): (a) 10; (b) 11