Question

two flower delivery services charge differently. - service a: $20 plus $8 per bouquet - service b: $12 per bouquet when does service a cost more than service b? what is the inequality for the problem? what is the solution? when does service a cost more than service b? write the answer as a sentence.

Explanation:

Step1: Define variables and cost functions

Let $x$ = number of bouquets.
Cost of Service A: $C_A = 20 + 8x$
Cost of Service B: $C_B = 12x$

Step2: Set up inequality for higher cost

We want $C_A > C_B$, so:
$20 + 8x > 12x$

Step3: Solve the inequality

Subtract $8x$ from both sides:
$20 > 4x$
Divide both sides by 4:
$\frac{20}{4} > x$
$5 > x$ or $x < 5$

Answer:

1. The inequality for the problem is $20 + 8x > 12x$
2. The solution to the inequality is $x < 5$
3. Service A costs more than Service B when the number of bouquets is less than 5.