In a club, a certain number of pupils can be arranged such that there are exactly 22 pupils per row. If the same number of pupils arranged in rows of 15 pupils each, there will be 5 more rows and 9 pupils left over. How many pupils are there altogether?
|
First arrangement |
Second arrangement |
Number |
1 u |
1 u + 5 |
Value |
22 |
15 |
Total value |
22 u |
15 u + 75 |
Total number of pupils in the first arrangement
= 1 u x 22
= 22 u
Total number of pupils in the second arrangement
= 15(1 u + 5)
= 15 u + 75
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.
22 u = 15 u + 75 + 9
22 u - 15 u = 84
7 u = 84
1 u = 84 ÷ 7 = 12
Total number of pupils
= 22 u
= 12 x 22
= 264
Answer(s): 264