Algebra Problem: Solving Charm Costs

How many charms would Becky need to add in order for the cost to be the same at either jewelry shop?

a) 6 charms
b) 7 charms
c) 8 charms
d) 9 charms
Final answer:

Explanation:

The cost at both Manchester Fine Jewelry and Castro Jewelers would be the same if Becky adds 8 charms. This is a problem of solving equations where we are to find the number of charms, i.e., when the cost at both jewelry shops would be the same.

At Manchester Fine Jewelry, the cost is $5 per charm plus $50 for the bracelet. At Castro Jewelers, the cost is $9 per charm plus $10 for the bracelet. If we let x represent the number of charms, we can set up the following equation that represents the cost:

5x + 50 = 9x + 10

By simplifying this equation, we find that x equals to 8. Therefore, the solution is c) 8 charms.

By adding 8 charms, the total cost at both jewelry shops would be the same, making it a point of balance in terms of cost for Becky.

Understanding algebraic equations and how to solve them is essential in various real-life scenarios, such as this jewelry cost comparison. It helps us make informed decisions and calculations based on different variables.