Some identical colouring books can be arranged in exactly 14 per row. If the same number of colouring books is arranged in rows of 9 colouring books each, there will be 6 more rows but short of 9 colouring books. How many colouring books are there altogether?
|
14 per row |
9 per row |
Number |
1 u |
1 u + 6 |
Value |
14 u |
9 |
Total value |
14 u |
9 u + 54 - 9 |
Number of rows if the colouring books are arranged in rows of 14 = 1 u
Number of rows if the colouring books are arranged in rows of 9 = 1 u + 6
Total number of colouring books if they are arranged in rows of 14
= 14 x 1 u
= 14 u
Total number of colouring books if they are arranged in rows of 9
= 9 x (1 u + 6) - 9
= 9 u + 54 - 9
= 9 u + 45
The total number of colouring books remains the same for both cases.
14 u = 9 u + 45
14 u - 9 u = 45
5 u = 45
1 u = 45 ÷ 5 = 9
Total number of colouring books
= 14 u
= 14 x 9
= 126
Answer(s): 126