Some identical novels can be arranged in exactly 11 per row. If the same number of novels is arranged in rows of 8 novels each, there will be 3 more rows and 6 novels left over. How many novels are there altogether?
| |
11 per row |
8 per row |
| Number |
1 u |
1 u + 3 |
| Value |
11 |
8 |
| Total value |
11 u |
8 u + 24 + 6 |
Number of rows if the novels are arranged in rows of 11 = 1 u
Number of rows if the novels are arranged in rows of 8 = 1 u + 3
Total number of novels if they are arranged in rows of 11
= 11 x 1 u
= 11 u
Total number of novels if they are arranged in rows of 8
= 8 x (1 u + 3) + 6
= 8 u + 24 + 6
= 8 u + 30
The total number of novels remains the same for both cases.
11 u = 8 u + 30
11 u - 8 u = 30
3 u = 30
1 u = 30 ÷ 3 = 10
Total number of novels
= 11 u
= 11 x 10
= 110
Answer(s): 110
