A box of marbles
A box contains red, blue, and green marbles. There are twice as many red marbles as blue marbles, and there are 5 more green marbles than blue marbles. If the total number of marbles is 37, how many of each colour marble are there?
The Riddle of the Rotating Satellite
A communication satellite orbits the Earth in a circular path. At a certain time, its shadow falls on a particular point on the Earth's surface. After 3 hours, the Earth has rotated 45 degrees, and the satellite has also completed a part of its orbit. If the satellite's shadow is now 1000 km away from the original point, calculate the radius of the satellite's orbit, assuming it remains constant and the Earth is a perfect sphere with a radius of 6400 km. Use the formula for the arc length in a circle, S=rθ, where S is the arc length, r is the radius, and θ is the angle in radians.
Let's call the number of blue marbles "b".
ReplyDeleteSince there are twice as many red marbles as blue marbles, the number of red marbles is 2b.
There are 5 more green marbles than blue marbles, so the number of green marbles is b + 5.
Given that the total number of marbles is 37, we can set up the equation:
b (blue) + 2b (red) + b + 5 (green) = 37
This simplifies to:
4b + 5 = 37
Subtracting 5 from both sides:
4b = 32
Dividing both sides by 4:
b = 8
So:
Blue marbles = 8
Red marbles = 2 x 8 = 16
Green marbles = 8 + 5 = 13
In summary:
Blue: 8
Red: 16
Green: 13