Question

two valentine card companies offer pricing plans. - company a: $15 plus $2 per card - company b: $4 per card for how many cards is company a cheaper than company b? what is the inequality for the problem? what is the solution? for how many cards is company a cheaper than company b? write the answer as a sentence.

Explanation:

Step1: Define cost functions

Let $x$ = number of cards.
Cost of Company A: $C_A = 15 + 2x$
Cost of Company B: $C_B = 4x$

Step2: Set up inequality for A cheaper

We want $C_A < C_B$, so:
$15 + 2x < 4x$

Step3: Solve the inequality

Subtract $2x$ from both sides:
$15 < 2x$
Divide both sides by 2:
$x > 7.5$
Since we cannot buy half a card, $x$ must be an integer greater than 7.5.

Answer:

The inequality for the problem is $15 + 2x < 4x$.
The solution is $x > 7.5$.
Company A is cheaper than Company B when purchasing 8 or more cards.