Math Tutorial

By: Dylan S.

Question:

Suppose you are going into business mowing lawns. You have purchased a lawn mower for $200. Gas and oil cost $1.50 per lawn. You are charging $15 per lawn. How many lawns must you mow for you to break-even?

Explanation:

First you must gather the important information. You will need to make 2 equations, one measuring you expenses and one measuring how much money you make. For the equation measuring expenses you have Y=total expenses and X=number of lawns mowed. You start off 200 dollars down, but since you are measuring expenses it is +200 dollars, not –200 dollars. And you have $1.50 for each lawn you mow. It should look something like this:

Y= total expenses

X= number of lawns mowed

Y= 1.5X+ 200

Next you must make an equation measuring your total amount of money you make. For this equations Y= total amount of money made and X= # of lawns mowed. For every lawn you mow you make 15 dollars. So you multiply X by 15. It should look something like this:

Y= total amount of money made

X= number of lawns mowed

Y=15X

We are looking for the point in which both the amount of money made and the expenses are the same. This is called the, “break-even point”. Also at this point the Y’s of each equation will be the same. So, this means that you can make the questions equal each other. It should look something like that:

X= number of lawns mowed

1.5X+200=15X

Now you must simplify the problem by taking away 1.5X from each side. After that you divide each side by 13.5 to get the value of X

1.5X+200=15X

-1.5X –1.5X

________________

200=13.5X

13.5 13.5

14.814 =(about) X

Another way to do this is the make a graph. To do this you make one line that goes up 1.5 for every X, its starts on the 200 on the y-axis line. The other line will go up 15 for every X. It should like this:

The numbers on the left is the amount of money. The X-axis represents the number of lawns mowed.

The answer is that the break-even point, or point in which both the expenses and money made is the same, is about 14.814. You would have to mow about 15 lawns (the rounded version of 14.814) to break-even. The cost will be about $222.22. This would make the break-even point (15, 222.22)