Can't figure this one out

Question

A kiosk in the mall sells Easter baskets. The fixed costs of operating the kiosk (rent, insurance, etc.) are $8,000. Each basket costs the store $4.75 and sells for $11.00.

(a) Rounding to the nearest whole basket, how many baskets must the store sell to break even?

(b) Rounding to the nearest whole basket, how many baskets must the store sell to make $2,000 in profit?

Answer 1

Let me read this with you slowly, piece by piece. First, I would ask you what is profit? I want to know how YOU would approach this problem, because there are many ways of approaching a problem.

Questions I would have you consider are...

For each basket what would be the profit (11b is the earning per basket, where b is the number of baskets) and subtracting 4.75b, the cost of each basket, will give you the profit for each basket sold, not including the fixed costs. 11-4.75 is 6.25b, or $6.25 is made for each basket sold. In addition to the 2,000 in profit, 8,000 more would have to be made to cover the fixed costs, so a total of 10,000 dollars would need to be made in profit for a 2000 dollar total profit. So we can simplify the problem to 6.25b = 10,000. Dividing 10,000 by 6.25 is the number of baskets we will need. I would ask the student how they approach it first and have the student write down on the whiteboard their notes so I can see how they organize their thoughts and get them to not rely on calculators but manually divide.

Answer 2

Let n be the number of Easter baskets sold.

The cost of selling the baskets is C = 8000 + 4.75n (they pay 8000 even if no Easter baskets are sold and each basket costs 4.75, so the cost of n baskets is 4.75n)

The earnings from selling Easter baskets is E = 11 n

The profit from selling Easter baskets is P = E - C = 11n - (8000 + 4.75n) = 6.25n - 8000

The break-even point is where E = C ==> 11n = 8000 + 4.75n ==> (11 - 4.75)n = 8000

n = 8000 / (11 - 4.75) = 1280

If there is a profit of $2000, then P = 2000 = 6.25n - 8000 ==> 10000 = 6.25n

==> n = 1600

An alternate method of finding the number of baskets is to divide 2000 by (11 - 4.75) then adding the result to 1280. 2000/6.25 = 320, 1280 + 320 = 1600

Answer 3

The kiosk makes $6.25 on each basket (11 - 4.25)

If b presents the number of baskets then

6.25b = 8000

Answer 4