There is a specialty store that you like to go to when you are craving jelly beans. The price is reasonable at $1.30 per pound. The store is a bit of a distance away and you could purchase the same jelly beans at your neighborhood supermarket, but the cost is a little more at $2.10 per pound. You spend about $3 on gas every time you go to the specialty store. How do you know if you are getting enough of the jelly beans to make the trip worthwhile? What two equations would you use to determine your break-even point? (Let C stand for the total cost and x represent the amount of jelly beans.)

-You know if you are getting enough of the jelly beans to make the trip worthwhile when the amount you purchased makes the total cost at the specialty store lower than the total cost at the supermarket and this is when you purchase more than 3.75 pounds of jelly beans.

-The two equations would be:

C=1.30x+3

C=2.10x

Explanation:

From the information given, the total cost at the specialty store would be the result of multiplying the price per pound for the number of pounds plus the amount you spend in gas everytime you go there, which is:

C=1.30x+3

Also, the total cost at your neighborhood supermarket would be the result of multiplying the price per pound for the number of pounds:

C=2.10x

Now, you can say that the price at the specialty store is equal to the price at the supermarket and solve for x to find the amount of jelly beans that would make the total cost at both places the same which would be the break-even point:

1.30x+3=2.10x

3=2.10x-1.30x

3=0.8x

x=3/0.8

x=3.75

You know if you are getting enough of the jelly beans to make the trip worthwhile when the amount you purchased makes the total cost at the specialty store lower than the total cost at the supermarket and this is when you purchase more than 3.75 pounds of jelly beans. Also, the two equations would be:

C=1.30x+3

C=2.10x