Some identical manuals can be arranged in exactly 12 per row. If the same number of manuals is arranged in rows of 7 manuals each, there will be 4 more rows and 2 manuals left over. How many manuals are there altogether?
| |
12 per row |
7 per row |
| Number |
1 u |
1 u + 4 |
| Value |
12 |
7 |
| Total value |
12 u |
7 u + 28 + 2 |
Number of rows if the manuals are arranged in rows of 12 = 1 u
Number of rows if the manuals are arranged in rows of 7 = 1 u + 4
Total number of manuals if they are arranged in rows of 12
= 12 x 1 u
= 12 u
Total number of manuals if they are arranged in rows of 7
= 7 x (1 u + 4) + 2
= 7 u + 28 + 2
= 7 u + 30
The total number of manuals remains the same for both cases.
12 u = 7 u + 30
12 u - 7 u = 30
5 u = 30
1 u = 30 ÷ 5 = 6
Total number of manuals
= 12 u
= 12 x 6
= 72
Answer(s): 72
