Some identical magazines can be arranged in exactly 13 per row. If the same number of magazines is arranged in rows of 10 magazines each, there will be 3 more rows but short of 3 magazines. How many magazines are there altogether?
| |
13 per row |
10 per row |
| Number |
1 u |
1 u + 3 |
| Value |
13 u |
10 |
| Total value |
13 u |
10 u + 30 - 3 |
Number of rows if the magazines are arranged in rows of 13 = 1 u
Number of rows if the magazines are arranged in rows of 10 = 1 u + 3
Total number of magazines if they are arranged in rows of 13
= 13 x 1 u
= 13 u
Total number of magazines if they are arranged in rows of 10
= 10 x (1 u + 3) - 3
= 10 u + 30 - 3
= 10 u + 27
The total number of magazines remains the same for both cases.
13 u = 10 u + 27
13 u - 10 u = 27
3 u = 27
1 u = 27 ÷ 3 = 9
Total number of magazines
= 13 u
= 13 x 9
= 117
Answer(s): 117
