Some identical guide books can be arranged in exactly 12 per row. If the same number of guide books is arranged in rows of 9 guide books each, there will be 3 more rows but short of 3 guide books. How many guide books are there altogether?
| |
12 per row |
9 per row |
| Number |
1 u |
1 u + 3 |
| Value |
12 u |
9 |
| Total value |
12 u |
9 u + 27 - 3 |
Number of rows if the guide books are arranged in rows of 12 = 1 u
Number of rows if the guide books are arranged in rows of 9 = 1 u + 3
Total number of guide books if they are arranged in rows of 12
= 12 x 1 u
= 12 u
Total number of guide books if they are arranged in rows of 9
= 9 x (1 u + 3) - 3
= 9 u + 27 - 3
= 9 u + 24
The total number of guide books remains the same for both cases.
12 u = 9 u + 24
12 u - 9 u = 24
3 u = 24
1 u = 24 ÷ 3 = 8
Total number of guide books
= 12 u
= 12 x 8
= 96
Answer(s): 96
