# Problem of the Day: 2/16/13

Congratulations to our Mathcounts team, who won 1st at the Shreveport competition and will advance to the state round in March!

On to the math problem,

What is the probability that the difference between the values on two dice rolled at the same time will be 2?

Solution to yesterday’s problem:

In order to find the value of y, we need to get an equation with y isolated on one side. Let’s use the first one, xy = 3. We also need to eliminate the x, so let’s substitute from the third equation, $xz=\frac{1}{27}$. Dividing by z,

$x=\frac{1}{27z}$

However, we want x to be in terms of y so the only variable in our final equation is y. So we’ll use the second equation, yz = 1. Dividing by y to isolate z,

$z=\frac{1}{y}$

Substituting for z in the last equation, we get

$x=\frac{1}{\frac{27}{y}}$

The y in the denominator moves to the numerator:

$x=\frac{y}{27}$

Substituting this into the first equation, xy = 3,

$\frac{y}{27}\times y=3$

$\frac{y^2}{27}=3$

$y^2=81$

$y=9$