# Problem of the Day: 2/20/13

Kelly walks her dog around her block in 20 minutes. She knows that 3 of these blocks is half a mile. In how many minutes can she walk her dog around her friend’s block, two of which constitute a mile?

Solution to yesterday’s problem:

Let’s represent the problem with two linear equations. The first one, the supply equation/curve, has a slope of 100,000 because that’s how many is added for each \$1 increase. So we can write that equation as

$y=100000x$

The demand equation has a y-intercept of 1,000,000 because that’s how many people would get the product at price zero. The slope is -300,000 because 300,000 less people would get it for each \$1 increase. So the demand equation is

$y=-300000x+1000000$

The point where supply and demand are equal is the intersection of these two lines. We can find this point by setting the two equations equal to each other:

$100000x=-300000x+1000000$

Solving this equation,

$400000x=1000000$

(Dividing by 100,000 to make the numbers a bit easier)

$4x=10$

$x=2.5$

So Company X should theoretically price Product X at exactly \$2.50.