Question

Jeremy opens a chocolate shop in the city. He pays $1,500 a month for rent and maintenance of the shop. The price of raw materials and manufacturing the chocolates is $6,000 a month. He sells the chocolates individually and in boxes of a dozen. Jeremy understands that his business needs a little time to become a success and decides that he wants to build a customer base initially. He is happy to break even for the first year. After a year, Jeremy prices his chocolates at $3 apiece. He offers a discount of 10% on boxes of chocolate to promote the sale of boxes. How many boxes of chocolate would he have to sell to recover the cost of running the business this year per month? (Assume that he sells no individual chocolates.)

Answer 1

To solve this problem you must apply the proccedure shown below:

1. Let's call
`x` to the number of boxes of chocolate.

2. You have that he spends for month:

`1500dollars+6000dollars=7500dollars`

3. The problem says that Jeremy prices his chocolates at
`3dollars` the piece and offers a discount of
`10`% on boxes of chocolate. Therefore, the price of a box is:

`36dollars-(36dollars)(0.1)=32.4dollars`

4. Therefore, you can write the following equation and solve for
`x`:

`32.4x=7500\\ x=232`

The answer is:
`232` boxes of chocolate.