Question

two chocolate subscription plans are compared. - plan a: $30 plus $5 per box - plan b: $8 per box when is plan a more expensive than plan b? what is the inequality for the problem? what is the solution? when is plan a more expensive than plan b? write the answer as a sentence.

Explanation:

Step1: Define variables and costs

Let $x$ = number of chocolate boxes.
Cost of Plan A: $30 + 5x$
Cost of Plan B: $8x$

Step2: Set up inequality for Plan A > Plan B

We want Plan A to be more expensive, so:
$$30 + 5x > 8x$$

Step3: Solve the inequality

Subtract $5x$ from both sides:
$$30 > 3x$$
Divide both sides by 3:
$$10 > x \quad \text{or} \quad x < 10$$

Answer:

What is the inequality for the problem?
$30 + 5x > 8x$

What is the solution?
$x < 10$

When is Plan A more expensive than Plan B?
Plan A is more expensive than Plan B when fewer than 10 boxes of chocolate are purchased.