Some identical colouring books can be arranged in exactly 11 per row. If the same number of colouring books is arranged in rows of 7 colouring books each, there will be 5 more rows but short of 3 colouring books. How many colouring books are there altogether?
| |
11 per row |
7 per row |
| Number |
1 u |
1 u + 5 |
| Value |
11 u |
7 |
| Total value |
11 u |
7 u + 35 - 3 |
Number of rows if the colouring books are arranged in rows of 11 = 1 u
Number of rows if the colouring books are arranged in rows of 7 = 1 u + 5
Total number of colouring books if they are arranged in rows of 11
= 11 x 1 u
= 11 u
Total number of colouring books if they are arranged in rows of 7
= 7 x (1 u + 5) - 3
= 7 u + 35 - 3
= 7 u + 32
The total number of colouring books remains the same for both cases.
11 u = 7 u + 32
11 u - 7 u = 32
4 u = 32
1 u = 32 ÷ 4 = 8
Total number of colouring books
= 11 u
= 11 x 8
= 88
Answer(s): 88
