Problema Solution
An algebra class has 112 students with an equal number of students in each row. If the desks are rearranged so there is one less row, there will be two more students in each row, How many rows were there originally? Let x=number of original rows and y=the number os students in each row
Answer provided by our tutors
Let
x = number of original rows, x>0
y = the number of students in each row
The total number of students is 112:
x*y = 112
y = 112/x
If there is 1 less row (x-1) there will be 2 more students in each row (y+2). But the total number of students still stays the same:
(x - 1)(y + 2) = 112
plug y = 112/x into the last equation:
(x - 1)(112/x + 2) = 112
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click here to see the equation solved for x
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x = 8 rows
We need to ignore the negative solution -7 since the number of rows can only be positive.
There were 8 rows originally.