Question

Can you help me with the denominator please!

Answer 1

`(1)/(19)`

Explanation:

Let's let B represent the amount of blue cubes, Y represent the amount of yellow cubes, and G represent the amount of green cubes.

We know that there are three times as many blue cubes as yellow cubes. In other words:

`B=3Y`

We also know that the are as five times as many green cubes as blue cubes. So:

`G=5B`

If Sarah takes a random cube, the chance it will be a yellow cube will be the total amount of yellow cubes over the total amount of cubes. In other words:

`P=(Y)/(Y+B+G)`

We can simplify this. Let's substitute 5B for G. This yields:

`P=(Y)/(Y+B+5B)`

Combine like terms:

`P=(Y)/(Y+6B)`

We can then substitute 3Y for B. This gives us:

`P=(Y)/(Y+6(3Y))`

Multiply:

`P=(Y)/(Y+18Y)`

Again, add:

`P=(Y)/(19Y)`

We can now cancel out the Y:

`P=(1)/(19)`

So, the chance of Sarah picking out a yellow cube is 1/19 or about 5.3% chance.

And we're done!