Some identical manuals can be arranged in exactly 15 per row. If the same number of manuals is arranged in rows of 9 manuals each, there will be 4 more rows and 6 manuals left over. How many manuals are there altogether?
| |
15 per row |
9 per row |
| Number |
1 u |
1 u + 4 |
| Value |
15 |
9 |
| Total value |
15 u |
9 u + 36 + 6 |
Number of rows if the manuals are arranged in rows of 15 = 1 u
Number of rows if the manuals are arranged in rows of 9 = 1 u + 4
Total number of manuals if they are arranged in rows of 15
= 15 x 1 u
= 15 u
Total number of manuals if they are arranged in rows of 9
= 9 x (1 u + 4) + 6
= 9 u + 36 + 6
= 9 u + 42
The total number of manuals remains the same for both cases.
15 u = 9 u + 42
15 u - 9 u = 42
6 u = 42
1 u = 42 ÷ 6 = 7
Total number of manuals
= 15 u
= 15 x 7
= 105
Answer(s): 105
