# Problem of the Day: 2/19/13

The company that makes Product X will make 100,000 units for every $1 increase in price. Two million people would buy the product if it were free, and 300,000 less people would buy it for every$1 increase in price. How should the Product X be priced so that there is no surplus or shortage?

Solution to yesterday’s problem:

First let’s find the rate at which each person works. Fred can mow a lawn in 3 hours; therefore, he can mow one-third of that lawn per hour. Following this, George can mow one-half of that lawn per hour. So their combined rates are

$\frac{1}{3}+\frac{1}{2}$

This simplifies to 5/6, or 5 lawns in 6 hours. We need to divide both numbers by 5 to find the time for one lawn: 5/5=1 and 6/5. So they will take 6/5 of an hour to mow the lawn; this simplifies to 1 1/5 hour, or 1 hour, 12 minutes.