Some identical guide books can be arranged in exactly 15 per row. If the same number of guide books is arranged in rows of 10 guide books each, there will be 3 more rows and 5 guide books left over. How many guide books 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 guide books are arranged in rows of 15 = 1 u
Number of rows if the guide books are arranged in rows of 10 = 1 u + 3
Total number of guide books if they are arranged in rows of 15
= 15 x 1 u
= 15 u
Total number of guide books 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 guide books 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 guide books
= 15 u
= 15 x 7
= 105
Answer(s): 105
