The probability that a cube has exactly two painted faces is 1/16. This is because if two adjacent sides are colored, then only the 4 cubes along the edge of those two sides are painted twice. 4/64 is 1/16.
The probability that a cube has no painted faces is 9/16. This is because if two adjacent sides are painted, then a total of 16 + 12= 28 cubes are painted on at least one side. We can also see this by subtracting 4 (the cubes overlapping) from 32 total cubes on two faces.
We multiply these two probabilities together because they are dependent events to get 9/256
First, let's start by creating a system of linear equations to solve. We know that both numbers added together equal 30, so we can write the equation x+y=30. [x and y represent our two numbers]
Now, for our second equation, we look at the second sentence of the problem. If x is doubled and we subtract (3y) we get 5. This can be written as 2x-3y=5.
To solve this equation, we will use substitution. We can move x to the other side of the equals sign in the first equation to get y= -x + 30.
This can be substituted into the second equasion as 2x - 3(-x+30)=5.
If simplified, this leads to 5x-90=5. If we bring 90 to the other side of the equals sign by adding 90 to both sides, we get 5x=95 or x=19.
Since x= 19, 30-19 = y. This means that y=11. The difference between 19 and 11 is 8.