Question

can you help me with the denominator please!

Answer 1

Answer:

$\frac{1}{19}$

Step-by-step 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:

$P=\frac{Y}{Y+B+G}$

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

$P=\frac{Y}{Y+B+5B}$

Combine like terms:

$P=\frac{Y}{Y+6B}$

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

$P=\frac{Y}{Y+6(3Y)}$

Multiply:

$P=\frac{Y}{Y+18Y}$

Again, add:

$P=\frac{Y}{19Y}$

We can now cancel out the Y:

$P=\frac{1}{19}$

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

And we're done!