In a class, a certain number of boys can be arranged such that there are exactly 21 boys per row. If the same number of boys arranged in rows of 13 boys each, there will be 5 more rows and 7 boys left over. How many boys are there altogether?
| |
First
arrangement |
Second
arrangement |
| Number |
1 u |
1 u + 5 |
| Value |
21 |
13 |
| Total value |
21 u |
13 u + 65 |
Total number of boys in the first arrangement
= 1 u x 21
= 21 u
Total number of boys in the second arrangement
= 13(1 u + 5)
= 13 u + 65
If 7 boys were included in the second arrangement, the total number of boys in the first arrangement and the second arrangement will be the same.
21 u = 13 u + 65 + 7
21 u - 13 u = 72
8 u = 72
1 u = 72 ÷ 8 = 9
Total number of boys
= 21 u
= 9 x 21
= 189
Answer(s): 189
