Question

You are comparing the costs of producing jewelry at two different manufacturers. Company 1 charges $3.25 per piece of jewelry plus a $400 flat fee. Company 2 charges $2.50 per pair piece of jewelry plus a $600 flat fee. How many pieces of jewelry are produced when the total costs for both companies are equal?Company 1 = $3.25x+400Company 2 = $2.50x+600Solve the following equation to determine when the costs are equal3.25x+400=2.50x+600

Answer 1

x = 266.67

Cost = $1266.67

Step-by-step explanation

We have that the equation that represents the situation that the total costs for each company is equal:

3.25x + 400 = 2.50x + 600

where x = pieces of jewelry

First, we have to find the number of pieces of jewelry, x.

To do that, we collect like terms:

3.25x - 2.5x = 600 - 400

0.75x = 200

Divide through by 0.75:

x = 200 / 0.75

x = 266.67 ≈ 267 pieces of jewelry

To find the value of the cost when the costs are equal, we have to solve either one of the equations.

Let us solve the first:

3.25 * (266.67) + 400

866.67 + 400

= $1266.67

That is the value of the cost when the costs are equal.