Some identical magazines can be arranged in exactly 14 per row. If the same number of magazines is arranged in rows of 9 magazines each, there will be 5 more rows but short of 5 magazines. How many magazines are there altogether?
|
14 per row |
9 per row |
Number |
1 u |
1 u + 5 |
Value |
14 u |
9 |
Total value |
14 u |
9 u + 45 - 5 |
Number of rows if the magazines are arranged in rows of 14 = 1 u
Number of rows if the magazines are arranged in rows of 9 = 1 u + 5
Total number of magazines if they are arranged in rows of 14
= 14 x 1 u
= 14 u
Total number of magazines if they are arranged in rows of 9
= 9 x (1 u + 5) - 5
= 9 u + 45 - 5
= 9 u + 40
The total number of magazines remains the same for both cases.
14 u = 9 u + 40
14 u - 9 u = 40
5 u = 40
1 u = 40 ÷ 5 = 8
Total number of magazines
= 14 u
= 14 x 8
= 112
Answer(s): 112