Some identical manuals can be arranged in exactly 13 per row. If the same number of manuals is arranged in rows of 9 manuals each, there will be 3 more rows and 5 manuals left over. How many manuals are there altogether?
| |
13 per row |
9 per row |
| Number |
1 u |
1 u + 3 |
| Value |
13 |
9 |
| Total value |
13 u |
9 u + 27 + 5 |
Number of rows if the manuals are arranged in rows of 13 = 1 u
Number of rows if the manuals are arranged in rows of 9 = 1 u + 3
Total number of manuals if they are arranged in rows of 13
= 13 x 1 u
= 13 u
Total number of manuals if they are arranged in rows of 9
= 9 x (1 u + 3) + 5
= 9 u + 27 + 5
= 9 u + 32
The total number of manuals remains the same for both cases.
13 u = 9 u + 32
13 u - 9 u = 32
4 u = 32
1 u = 32 ÷ 4 = 8
Total number of manuals
= 13 u
= 13 x 8
= 104
Answer(s): 104
