Question

two gift basket options are available.

• option a: $25 plus $6 per item
• option b: $9 per item

for how many items does option a cost more than option b?
what is the inequality for the problem?
what is the solution?
for how many items does option a cost more than option b? write the answer as a sentence.

Explanation:

Step1: Define cost expressions

Let $x$ = number of items.
Cost of Option A: $25 + 6x$
Cost of Option B: $9x$

Step2: Set up inequality

We want Option A > Option B:
$25 + 6x > 9x$

Step3: Solve the inequality

Subtract $6x$ from both sides:
$25 > 3x$
Divide both sides by 3:
$x < \frac{25}{3} \approx 8.33$

Step4: Interpret the solution

Since $x$ must be a positive whole number of items, $x$ can be 1, 2, 3, 4, 5, 6, 7, 8.

Answer:

Inequality: $25 + 6x > 9x$
Solution: $x < \frac{25}{3}$
Option A costs more than Option B when the number of items is less than 9 (specifically 1 to 8 items).