Some identical novels can be arranged in exactly 14 per row. If the same number of novels is arranged in rows of 10 novels each, there will be 3 more rows and 2 novels left over. How many novels are there altogether?
| |
14 per row |
10 per row |
| Number |
1 u |
1 u + 3 |
| Value |
14 |
10 |
| Total value |
14 u |
10 u + 30 + 2 |
Number of rows if the novels are arranged in rows of 14 = 1 u
Number of rows if the novels are arranged in rows of 10 = 1 u + 3
Total number of novels if they are arranged in rows of 14
= 14 x 1 u
= 14 u
Total number of novels if they are arranged in rows of 10
= 10 x (1 u + 3) + 2
= 10 u + 30 + 2
= 10 u + 32
The total number of novels remains the same for both cases.
14 u = 10 u + 32
14 u - 10 u = 32
4 u = 32
1 u = 32 ÷ 4 = 8
Total number of novels
= 14 u
= 14 x 8
= 112
Answer(s): 112
