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?
Solve the simultaneous equations.
Given that x and y are positive integers, solve the simultaneous equations: 3^x * 2^y = 72 3^(x-1) * 2^(y+1) = 48
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