Some identical magazines can be arranged in exactly 12 per row. If the same number of magazines is arranged in rows of 7 magazines each, there will be 6 more rows and 3 magazines left over. How many magazines are there altogether?
| |
12 per row |
7 per row |
| Number |
1 u |
1 u + 6 |
| Value |
12 |
7 |
| Total value |
12 u |
7 u + 42 + 3 |
Number of rows if the magazines are arranged in rows of 12 = 1 u
Number of rows if the magazines are arranged in rows of 7 = 1 u + 6
Total number of magazines if they are arranged in rows of 12
= 12 x 1 u
= 12 u
Total number of magazines if they are arranged in rows of 7
= 7 x (1 u + 6) + 3
= 7 u + 42 + 3
= 7 u + 45
The total number of magazines remains the same for both cases.
12 u = 7 u + 45
12 u - 7 u = 45
5 u = 45
1 u = 45 ÷ 5 = 9
Total number of magazines
= 12 u
= 12 x 9
= 108
Answer(s): 108
