In the school hall, chairs were arranged in rows of 11. During a function, 40 chairs were added to accommodate the number of people. The chairs were rearranged to form rows of 9. As a result, there were 6 more rows.
- How many chairs were there in the extra 6 rows?
- How many chairs were there in the school hall in the end?
|
First arrangement |
Second arrangement |
Number |
1 u |
1 u + 6 |
Value |
11 |
9 |
Total value |
11 u |
9 u + 54 |
(a)
Number of chairs in the extra 6 rows
= 6 x 9
= 54
(b)
Total number of chairs in the first arrangement
= 1 u x 11
= 11 u
Total number of chairs in the second arrangement
= 9(1 u + 6)
= 9 u + 54
If 40 chairs were included in the first arrangement, the total number of chairs in the first arrangement and the second arrangement will be the same.
11 u + 40 = 9 u + 54
11 u - 9 u = 54 - 40
2 u = 14
1 u = 14 ÷ 2 = 7
Number of chairs in the school hall in the end
= 7 x 11 + 40
= 77 + 40
= 117
Answer(s): (a) 54; (b) 117