Some identical colouring books can be arranged in exactly 13 per row. If the same number of colouring books is arranged in rows of 8 colouring books each, there will be 3 more rows and 6 colouring books left over. How many colouring books are there altogether?
| |
13 per row |
8 per row |
| Number |
1 u |
1 u + 3 |
| Value |
13 |
8 |
| Total value |
13 u |
8 u + 24 + 6 |
Number of rows if the colouring books are arranged in rows of 13 = 1 u
Number of rows if the colouring books are arranged in rows of 8 = 1 u + 3
Total number of colouring books if they are arranged in rows of 13
= 13 x 1 u
= 13 u
Total number of colouring books 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 colouring books remains the same for both cases.
13 u = 8 u + 30
13 u - 8 u = 30
5 u = 30
1 u = 30 ÷ 5 = 6
Total number of colouring books
= 13 u
= 13 x 6
= 78
Answer(s): 78
