Question

The school band sells carnations on Valentine's Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge. Solve this using systems of equations. When will the cost of the carnations be equal to the revenue from selling them?

Answer 1

To find when the cost equals revenue for the school band selling carnations, we use the system of equations: Cost = 0.50x + 16 and Revenue = 2x. Solving for x, we discover that the band needs to sell at least 11 carnations to break even.

Step-by-step explanation:

The student is asking about solving a problem using systems of equations, particularly to find out when the cost of carnations will be equal to the revenue from selling them. We can set this up as two equations to represent the cost and revenue.

Let's define x as the number of carnations.

The cost equation (total cost) is the sum of the purchase cost and the delivery charge: Cost = 0.50x + 16.

The revenue equation (total revenue) is simply the number of carnations sold multiplied by the selling price: Revenue = 2x.

To find out when the cost and revenue are equal, we can set up an equation: 0.50x + 16 = 2x. Solving for x, we get:

2x - 0.50x = 16
x = 16 / 1.5
x = 10.67

Since we cannot sell a fraction of a carnation, we would round up to 11. So, the band needs to sell at least 11 carnations for the cost to equal the revenue.