Some identical textbooks can be arranged in exactly 12 per row. If the same number of textbooks is arranged in rows of 8 textbooks each, there will be 3 more rows and 4 textbooks left over. How many textbooks are there altogether?
| |
12 per row |
8 per row |
| Number |
1 u |
1 u + 3 |
| Value |
12 |
8 |
| Total value |
12 u |
8 u + 24 + 4 |
Number of rows if the textbooks are arranged in rows of 12 = 1 u
Number of rows if the textbooks are arranged in rows of 8 = 1 u + 3
Total number of textbooks if they are arranged in rows of 12
= 12 x 1 u
= 12 u
Total number of textbooks if they are arranged in rows of 8
= 8 x (1 u + 3) + 4
= 8 u + 24 + 4
= 8 u + 28
The total number of textbooks remains the same for both cases.
12 u = 8 u + 28
12 u - 8 u = 28
4 u = 28
1 u = 28 ÷ 4 = 7
Total number of textbooks
= 12 u
= 12 x 7
= 84
Answer(s): 84
