Question

two candy stores offer different pricing. - store a: $10 plus $3 per box - store b: $5 per box for how many boxes is store a more expensive than store b? what is the inequality for the problem? what is the solution? for how many boxes is store a more expensive than store b? write the answer as a sentence.

Explanation:

Step1: Define variables and cost functions

Let $x$ = number of candy boxes.
Cost of Store A: $C_A = 10 + 3x$
Cost of Store B: $C_B = 5x$

Step2: Set up inequality for Store A costlier

We want $C_A > C_B$, so:
$10 + 3x > 5x$

Step3: Solve the inequality

Subtract $3x$ from both sides:
$10 > 2x$
Divide both sides by 2:
$x < 5$

Step4: Interpret the solution

Since $x$ is a positive whole number of boxes, $x$ can be 1, 2, 3, 4.

Answer:

1. Inequality: $10 + 3x > 5x$
2. Solution: $x < 5$
3. Store A is more expensive than Store B when purchasing 1, 2, 3, or 4 boxes of candy.