Question

Manchester Fine Jewelry charges $5 per charm plus $50 for the bracelet. Castro jewelers in contrast charges $9 per charm and $10 for the bracelet How many charms would Becky need to add in order for the cost to be the same at either jewelry shop

Answer 1

Let's set up equations for the total cost at each jewelry shop based on the number of charms Becky purchases.

Let \( x \) be the number of charms.

**Cost at Manchester Fine Jewelry:**
The cost for the bracelet is $50, and each charm costs $5. So the total cost can be expressed as:
\[
\text{Cost at Manchester} = 50 + 5x
\]

**Cost at Castro Jewelers:**
The cost for the bracelet is $10, and each charm costs $9. So the total cost can be expressed as:
\[
\text{Cost at Castro} = 10 + 9x
\]

To find the number of charms \( x \) where the costs are the same, we set the two expressions equal to each other:
\[
50 + 5x = 10 + 9x
\]

Now, we'll solve for \( x \):

1. Subtract \( 5x \) from both sides:
\[
50 = 10 + 4x
\]

2. Subtract \( 10 \) from both sides:
\[
40 = 4x
\]

3. Divide by \( 4 \):
\[
x = 10
\]

Therefore, Becky would need to add **10 charms** for the cost to be the same at both jewelry shops.