Question

Write and solve a system of equations to solve the problem. A small costume business spends $550 for start-up costs and $15 per costume. The business sells each costume for $20. Choose and solve a system of equations to find the break-even point for the business.

Answer 1

The break- even point for the business is 110 number of constumes .

Explanation:

Definition of break-even point

The break even point is the production unit where total revenues equals total expenses.

As given

A small costume business spends $550 for start-up costs and $15 per costume.

The business sells each costume for $20.

Let us assume that the number of costume be v .

Let us assume that the u represented the total cost of expense or income .

Equstion becomes

Total expense = Business start-up cost + Number of costumes × Price of per costumes .

u =550 + 15v

Total income = Number of costumes × Selling Price of per costumes .

u = 20v

Two equations becomes

u =550 + 15v

u = 20v

Compare above equations

20v = 550 + 15v

20v - 15v = 550

5v = 550

`v = (550)/(5)`

v = 110

Therefore the break- even point for the business is 110 number of constumes .