Some identical guide books can be arranged in exactly 10 per row. If the same number of guide books is arranged in rows of 7 guide books each, there will be 3 more rows and 6 guide books left over. How many guide books are there altogether?
| |
10 per row |
7 per row |
| Number |
1 u |
1 u + 3 |
| Value |
10 |
7 |
| Total value |
10 u |
7 u + 21 + 6 |
Number of rows if the guide books are arranged in rows of 10 = 1 u
Number of rows if the guide books are arranged in rows of 7 = 1 u + 3
Total number of guide books if they are arranged in rows of 10
= 10 x 1 u
= 10 u
Total number of guide books if they are arranged in rows of 7
= 7 x (1 u + 3) + 6
= 7 u + 21 + 6
= 7 u + 27
The total number of guide books remains the same for both cases.
10 u = 7 u + 27
10 u - 7 u = 27
3 u = 27
1 u = 27 ÷ 3 = 9
Total number of guide books
= 10 u
= 10 x 9
= 90
Answer(s): 90
