Question

Lucas is selling ribbons to raise money for the Juvenile Diabetes Research Foundation. His expenses include $24 for materials, plus $0.04 per ribbon. If Lucas charges $0.50 per ribbon, how many ribbons does he need to sell to break even? Write a system of equations that represents the situation. Let x represent the number of ribbons, and let y represent the expense or revenue. Solve the system of equations.

Answer 1

Let's set up a system of equations to represent the situation:

Expense equation: y = 0.04x + 24

Revenue equation: y = 0.50x

The expense equation represents Lucas's total expenses, which includes $24 for materials and $0.04 for each ribbon sold. The revenue equation represents the total revenue from selling x ribbons at $0.50 per ribbon.

To find the number of ribbons Lucas needs to sell to break even, we need to set the revenue equation equal to the expense equation:

0.04x + 24 = 0.50x

Subtracting 0.04x from both sides, we get:

24 = 0.46x

Dividing both sides by 0.46, we get:

x = 52.17

Since Lucas cannot sell a fraction of a ribbon, he needs to sell at least 53 ribbons to break even.

So, Lucas needs to sell at least 53 ribbons to cover his expenses and break even.