Some identical textbooks can be arranged in exactly 10 per row. If the same number of textbooks is arranged in rows of 7 textbooks each, there will be 3 more rows and 6 textbooks left over. How many textbooks are there altogether?
|
10 per row |
7 per row |
Number |
1 u |
1 u + 3 |
Value |
10 |
7 |
Total value |
10 u |
7 u + 21 + 6 |
Number of rows if the textbooks are arranged in rows of 10 = 1 u
Number of rows if the textbooks are arranged in rows of 7 = 1 u + 3
Total number of textbooks if they are arranged in rows of 10
= 10 x 1 u
= 10 u
Total number of textbooks if they are arranged in rows of 7
= 7 x (1 u + 3) + 6
= 7 u + 21 + 6
= 7 u + 27
The total number of textbooks remains the same for both cases.
10 u = 7 u + 27
10 u - 7 u = 27
3 u = 27
1 u = 27 ÷ 3 = 9
Total number of textbooks
= 10 u
= 10 x 9
= 90
Answer(s): 90