You are the advisor of a Junior Achievement group in a local high school. You need to help the group make a decision about fees that must be paid to sell gardening tools at the Home and Garden Show. The group sells a set of tools for $24.00. The manufacturing cost (all variable) is $7.20 per set. The Home and Garden Show coordinator allows the following payment option for groups exhibiting and selling at the show:

Pay a fee of $4,560 plus 10% of all revenue from tool sets sold at the show.

how many sets do they have to sell to break even

Question

You are the advisor of a Junior Achievement group in a local high school. You need to help the group make a decision about fees that must be paid to sell gardening tools at the Home and Garden Show. The group sells a set of tools for $24.00. The manufacturing cost (all variable) is $7.20 per set. The Home and Garden Show coordinator allows the following payment option for groups exhibiting and selling at the show:

Pay a fee of $4,560 plus 10% of all revenue from tool sets sold at the show.

how many sets do they have to sell to break even

whpalmer4 · Answer

let's figure it out!  

if we sell $x$ sets, the revenue will be $24x$

cost of goods sold will be manufacturing cost + selling cost
COGS = $7.20x + 4560 + 0.10*24x$

At break-even, revenue = COGS
$$24x = 7.20x + 4560 + 2.4x$$

Solve for $x$, then check your work by plugging in the value of $x$ and making sure that the revenue and cost numbers match.