Some identical workbooks can be arranged in exactly 12 per row. If the same number of workbooks is arranged in rows of 9 workbooks each, there will be 3 more rows but short of 9 workbooks. How many workbooks 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 - 9 |
Number of rows if the workbooks are arranged in rows of 12 = 1 u
Number of rows if the workbooks are arranged in rows of 9 = 1 u + 3
Total number of workbooks if they are arranged in rows of 12
= 12 x 1 u
= 12 u
Total number of workbooks if they are arranged in rows of 9
= 9 x (1 u + 3) - 9
= 9 u + 27 - 9
= 9 u + 18
The total number of workbooks remains the same for both cases.
12 u = 9 u + 18
12 u - 9 u = 18
3 u = 18
1 u = 18 ÷ 3 = 6
Total number of workbooks
= 12 u
= 12 x 6
= 72
Answer(s): 72