Question

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.)

Answer 1

To determine if the specialty store trip is worth it, calculate the break-even point by setting the total cost equations from both stores equal to each other (1.30x + 3 = 2.10x) and solve for the number of jelly beans. The break-even quantity comes out to be 3.75 pounds.

Step-by-step explanation:

To determine whether it is worth it to travel to the specialty store for jelly beans, we need to compare the total cost of purchasing jelly beans at both stores. We need two equations to establish the break-even point. The first equation will calculate the cost of purchasing jelly beans at the specialty store plus the cost of gas:

C = 1.30x + 3

The second equation will calculate the cost at the neighborhood supermarket without the gas cost:

C = 2.10x

To find the break-even quantity of jelly beans, we set these two equations equal to each other and solve for x:

1.30x + 3 = 2.10x

We subtract 1.30x from both sides:

3 = 0.80x

Finally, we divide by 0.80 to solve for x:

x = 3 ÷ 0.80

x = 3.75 pounds

Therefore, you would need to purchase at least 3.75 pounds of jelly beans for the trip to the specialty store to be cost-effective.