Some identical textbooks can be arranged in exactly 14 per row. If the same number of textbooks is arranged in rows of 10 textbooks each, there will be 3 more rows and 6 textbooks left over. How many textbooks are there altogether?
| |
14 per row |
10 per row |
| Number |
1 u |
1 u + 3 |
| Value |
14 |
10 |
| Total value |
14 u |
10 u + 30 + 6 |
Number of rows if the textbooks are arranged in rows of 14 = 1 u
Number of rows if the textbooks are arranged in rows of 10 = 1 u + 3
Total number of textbooks if they are arranged in rows of 14
= 14 x 1 u
= 14 u
Total number of textbooks if they are arranged in rows of 10
= 10 x (1 u + 3) + 6
= 10 u + 30 + 6
= 10 u + 36
The total number of textbooks remains the same for both cases.
14 u = 10 u + 36
14 u - 10 u = 36
4 u = 36
1 u = 36 ÷ 4 = 9
Total number of textbooks
= 14 u
= 14 x 9
= 126
Answer(s): 126
