Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Herman is starting a business selling handmade necklaces. He has decided to invest an initial amount of $21 for advertising, and materials cost $8 for each necklace he makes. Herman can sell his creations for $9 per necklace. Once he makes and sells a certain number of necklaces, he will break even, with identical expenses and sales. How many necklaces would that take?

What would the total expenses and sales be then? After selling____necklaces, Herman would have total expenses and sales of $____

Answer 1

To break even, Herman would need to make and sell 21 necklaces, resulting in total expenses of $168 and total sales of $189.

Step-by-step explanation:

To write a system of equations to describe Herman's situation, let's assign some variables:

- Let x represent the number of necklaces Herman makes and sells.

- The cost of materials for each necklace is $8, so the total cost of materials would be 8x.

- Herman sells each necklace for $9, so the total revenue from selling necklaces would be 9x.

- The initial investment for advertising is $21.

Since Herman wants to break even, the total expenses and sales would be equal. Therefore, we can set up the following equation:

8x + 21 = 9x

To solve this equation using substitution, we can subtract 8x from both sides:

21 = x

So, Herman would need to make and sell 21 necklaces in order to break even.

The total expenses and sales can be calculated by substituting the value of x into the expressions for expenses and sales:

Total expenses = 8x = 8 * 21 = $168

Total sales = 9x = 9 * 21 = $189