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Boys of a scout group want to stand in rows. If one scout is added in each row then number of rows will be reduced by two,
but if one scout is reduced from each row, we will need three more rows. What is the total scout count in the group?
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The governing equations are
nr = (n+1)*(r-2), (1)
nr = (n-1)*(r+3). (2)
where "r" is the number of scouts in the row at the basic scenario,
"n" is the number of rows at the basic scenario.
Simplify (1) and (2) step by step:
nr = nr + r - 2n - 2, (3) ( instead of (1) )
nr = nr - r + 3n - 3. (4) ( instead of (2) )
0 = r - 2n - 2, (5) ( instead of (3) )
0 = -r + 3n - 3, (6) ( instead of (4) )
r - 2n = 2, (7) ( instead of (5) )
-r + 3n = 3. (8) ( instead of (6) )
Add equations (7) and (8). You will get n = 5.
Then from (7) r = 2 + 2n = 2 + 2*5 = 12.
The total scout count in the group is 12*5 = 60.
Answer. The total scout count in the group is 60.