Some identical magazines can be arranged in exactly 15 per row. If the same number of magazines is arranged in rows of 10 magazines each, there will be 3 more rows and 5 magazines left over. How many magazines are there altogether?
| |
15 per row |
10 per row |
| Number |
1 u |
1 u + 3 |
| Value |
15 |
10 |
| Total value |
15 u |
10 u + 30 + 5 |
Number of rows if the magazines are arranged in rows of 15 = 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 15
= 15 x 1 u
= 15 u
Total number of magazines if they are arranged in rows of 10
= 10 x (1 u + 3) + 5
= 10 u + 30 + 5
= 10 u + 35
The total number of magazines remains the same for both cases.
15 u = 10 u + 35
15 u - 10 u = 35
5 u = 35
1 u = 35 ÷ 5 = 7
Total number of magazines
= 15 u
= 15 x 7
= 105
Answer(s): 105
