A clock shop has three cuckoo clocks on display. The cuckoo's appear at different time intervals. One comes out every 25 minutes, one comes out every 30 minutes, and one comes out every 60 minutes. If they all appear at 5 o'clock, what is the next time they will all come out together

First, let's make a system of equations.

x = roller coaster
y = ferris wheel

x + y = 12
5x + 3y = 50

Solve for x in the first equation.

x + y = 12

Subtract y from both sides.

x = 12 - y

Substitute this into the second equation in place of x.

5(12 - y) + 3y = 50

Simplify.

60 - 5y + 3y = 50

Combine like terms.

60 - 2y = 50

Subtract 60 from both sides.

-2y = -10

Divide -2 on both sides.

y = 5

Substitute 5 in place of y in the first equation.

x + 5 = 12

Subtract 5 from both sides.

x = 7

Let's check the work by putting these values into the second equation.

5(7) + 3(5) = 50
35 + 15 = 50
50 = 50

So you can ride the ferris wheel 5 times and the roller coaster 7 times.

Hope this helps! :)