Some identical colouring books can be arranged in exactly 13 per row. If the same number of colouring books is arranged in rows of 10 colouring books each, there will be 3 more rows but short of 3 colouring books. How many colouring books are there altogether?
| |
13 per row |
10 per row |
| Number |
1 u |
1 u + 3 |
| Value |
13 u |
10 |
| Total value |
13 u |
10 u + 30 - 3 |
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 10 = 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 10
= 10 x (1 u + 3) - 3
= 10 u + 30 - 3
= 10 u + 27
The total number of colouring books remains the same for both cases.
13 u = 10 u + 27
13 u - 10 u = 27
3 u = 27
1 u = 27 ÷ 3 = 9
Total number of colouring books
= 13 u
= 13 x 9
= 117
Answer(s): 117
