In a club, a certain number of pupils can be arranged such that there are exactly 21 pupils per row. If the same number of pupils arranged in rows of 13 pupils each, there will be 3 more rows and 9 pupils left over. How many pupils are there altogether?
| |
First
arrangement |
Second
arrangement |
| Number |
1 u |
1 u + 3 |
| Value |
21 |
13 |
| Total value |
21 u |
13 u + 39 |
Total number of pupils in the first arrangement
= 1 u x 21
= 21 u
Total number of pupils in the second arrangement
= 13(1 u + 3)
= 13 u + 39
If 9 pupils were included in the second arrangement, the total number of pupils in the first arrangement and the second arrangement will be the same.
21 u = 13 u + 39 + 9
21 u - 13 u = 48
8 u = 48
1 u = 48 ÷ 8 = 6
Total number of pupils
= 21 u
= 6 x 21
= 126
Answer(s): 126
