A rectangular classroom seats 252 students. If the seats were rearranged with three more seats in each row, the classroom would have two fewer rows. Find the original number of seats in each row.
(x+3)(252/x - 2) = 252
x = 18
Check: 18*14 = 21*12 = 252
tang ina ang hirap naman!
504
A theater has room for 100 people inside. During the last show, the theater was only filled 60% capacity. How many tickets were not sold for the last show?
9 seats per row
To solve this problem, let's first assume that there are 'x' seats in each row of the classroom.
If the classroom seats 252 students, then the total number of seats can be calculated by multiplying the number of rows 'r' with the number of seats in each row 'x': r * x = 252.
According to the problem, if there were three more seats in each row, and two fewer rows, the new arrangement would have (x + 3) seats in each row and (r - 2) rows.
We can construct a second equation using the new arrangement: (r - 2) * (x + 3).
Based on the given information, we know that the total number of seats remains the same in both arrangements.
Setting the two equations equal to each other, we have: r * x = (r - 2) * (x + 3).
Expanding this equation, we get: rx = rx + 3r - 2x - 6.
Canceling out the common terms 'rx' on both sides of the equation, we get: 0 = 3r - 2x - 6.
Rearranging the equation, we have: 2x = 3r - 6.
Simplifying further, we get: 2x = 3(r - 2).
Dividing both sides of the equation by 2, we get: x = (3/2)(r - 2).
Since 'x' represents the number of seats in each row, 'x' must be a whole number. This means that (r - 2) has to be divisible by 2, or (r - 2) must be an even number.
Now, let's take a look at the prime factorization of 252, to find the possible values for 'r' and 'x'.
Prime factorization of 252: 252 = 2 * 2 * 3 * 3 * 7.
We can pair the prime factors into possible values for 'r' and 'x':
- r = 1 * 7
x = (3 * 2 * 3) / 2 = 3 * 3 = 9
- r = 2 * 3
x = (3 * 7 * 3) / 2 = 9 * 7 = 63
- r = 2 * 7
x = (3 * 3 * 3) / 2 = 9 * 3 = 27
- r = 3 * 3
x = (2 * 7 * 3) / 2 = 7 * 3 = 21
Notice that for the value of 'x' to be a whole number, 'r' must be even. Therefore, 'r' cannot equal 1, as there would be an odd number of rows.
Hence, the original number of seats in each row of the classroom is 9.