Question

1. the school band sells carnations on valentine’s day for $2 each. it buys the carnations from a florist for $0.50 each, plus a $16 delivery charge. when will the cost of the carnations be equal to the revenue from selling them? how many carnations does it need to sell to reach this point?

Explanation:

Step1: Define Variables

Let \( x \) be the number of carnations. Cost \( C = 0.5x + 16 \), Revenue \( R = 2x \). Set \( C = R \).

Step2: Set Up Equation

\( 0.5x + 16 = 2x \)

Step3: Solve for \( x \)

Subtract \( 0.5x \): \( 16 = 1.5x \). Divide by \( 1.5 \): \( x = \frac{16}{1.5}=\frac{32}{3}\approx10.67 \). Since we need whole carnations, round up to \( 11 \) (or check \( x = 11 \): \( C = 0.5(11)+16 = 21.5 \), \( R = 22 \); \( x = 10 \): \( C = 21 \), \( R = 20 \)). So \( x = 11 \) (or exact fraction \( \frac{32}{3} \), but practical is 11).

Answer:

The school band needs to sell 11 carnations (or \( \boldsymbol{\frac{32}{3}\approx10.67} \), but 11 for practical purposes) to reach the break - even point.