Question

two party decoration companies have different prices. - company a: $40 plus $2 per decoration - company b: $6 per decoration for how many decorations is company a cheaper than company b? what is the inequality for the problem? what is the solution? for how many decorations is company a cheaper than company b? write the answer as a sentence.

Explanation:

Step1: Define variables and cost functions

Let $x$ = number of decorations.
Cost of Company A: $C_A = 40 + 2x$
Cost of Company B: $C_B = 6x$

Step2: Set up inequality for Company A cheaper

We want $C_A < C_B$, so:
$40 + 2x < 6x$

Step3: Solve the inequality

Subtract $2x$ from both sides:
$40 < 4x$
Divide both sides by 4:
$x > 10$

Step4: Interpret the solution

Since $x$ must be a positive integer (number of decorations), Company A is cheaper when the number of decorations is greater than 10.

Answer:

1. Inequality: $40 + 2x < 6x$
2. Solution: $x > 10$
3. Company A is cheaper than Company B when the number of decorations is greater than 10.