Question

a jewelry store charges $45 plus $15 per charm added to a bracelet. you want the bracelet to cost more than $150. what is the inequality for the problem? what is the solution? how many charms must be added? write the answer as a sentence.

Explanation:

Step1: Define variable & inequality

Let $x$ = number of charms. Total cost is base cost plus per-charm cost, which must exceed $150:
$45 + 15x > 150$

Step2: Isolate the variable term

Subtract 45 from both sides:
$15x > 150 - 45$
$15x > 105$

Step3: Solve for x

Divide both sides by 15:
$x > \frac{105}{15}$
$x > 7$

Step4: Interpret the solution

Since charms are whole items, $x$ must be an integer greater than 7.

Answer:

1. Inequality: $45 + 15x > 150$
2. Solution: $x > 7$
3. 8 or more charms must be added to make the bracelet cost more than $150.