A movie theater just added two rooms. One room is large enough for 125 people, and the other can seat up to 350 people. In each room, the seating is arranged in horizontal rows with the same number of seats in each row. what is the greatest number of seats that can make up each row?
It sounds to me as if you need to work out the highest common factor (HCF) of 125 and 300, which I think is 25, since 125 = 5 x 25, and 300 = 12 x 25. If so, you'll have 25 seats in each row, with 5 rows in the first room, and 12 rows in the second.
To find the greatest number of seats that can make up each row in the smaller room, we need to find the factors of 125.
The factors of 125 are: 1, 5, 25, 125.
Since the seating is arranged in horizontal rows, we need to consider the possibility of having 1 seat in each row, which would result in only 125 rows.
If we consider having 5 seats in each row, we would have 25 rows.
If we consider having 25 seats in each row, we would have 5 rows.
If we consider having all 125 seats in a single row, it would not be a horizontal arrangement. Therefore, the greatest number of seats that can make up each row in the smaller room is 25.
To find the greatest number of seats that can make up each row in the movie theater rooms, we need to find the common factor of both 125 and 350.
First, let's find the factors of 125. The factors of 125 are 1, 5, 25, and 125.
Next, let's find the factors of 350. The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350.
Looking at the common factors, we can see that 5 is the greatest common factor between 125 and 350. Therefore, the largest number of seats in each row would be 5.
Hence, the greatest number of seats that can make up each row in the movie theater rooms is 5.