Math Problems, Probability Problems

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

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s