In a group, a certain number of friends can be arranged such that there are exactly 27 friends per row. If the same number of friends arranged in rows of 17 friends each, there will be 5 more rows and 5 friends left over. How many friends are there altogether?
| |
First
arrangement |
Second
arrangement |
| Number |
1 u |
1 u + 5 |
| Value |
27 |
17 |
| Total value |
27 u |
17 u + 85 |
Total number of friends in the first arrangement
= 1 u x 27
= 27 u
Total number of friends in the second arrangement
= 17(1 u + 5)
= 17 u + 85
If 5 friends were included in the second arrangement, the total number of friends in the first arrangement and the second arrangement will be the same.
27 u = 17 u + 85 + 5
27 u - 17 u = 90
10 u = 90
1 u = 90 ÷ 10 = 9
Total number of friends
= 27 u
= 9 x 27
= 243
Answer(s): 243
