Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Bridgette wants to buy a charm bracelet. Lancaster Fine Jewelry charges $17 per charm, plus $17 for the bracelet. Bradshaw Jewelers, in contrast, charges $15 per charm and $21 for the bracelet. If Bridgette wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. How many charms would that be? What would the total cost of the bracelet be?


If Bridgette adds
charms to her bracelet, it will cost $
at either shop.

Answer 1

Let's define the number of charms Bridgette wants to buy as \( x \).

### Step 1: Write the equations

1. **Cost at Lancaster Fine Jewelry:** The cost consists of the cost of the bracelet and the cost of the charms:
\[
C_1 = 17x + 17
\]

2. **Cost at Bradshaw Jewelers:** Similarly, the total cost here is:
\[
C_2 = 15x + 21
\]

### Step 2: Set up the equation

To find out when the costs are equal, we set the two equations equal to each other:
\[
17x + 17 = 15x + 21
\]

### Step 3: Solve for \( x \)

1. Subtract \( 15x \) from both sides:
\[
2x + 17 = 21
\]

2. Subtract 17 from both sides:
\[
2x = 4
\]

3. Divide by 2:
\[
x = 2
\]

### Step 4: Calculate the total cost

Now that we know \( x = 2 \), we can calculate the total cost at either jewelry shop.

Using either equation:
- Cost at Lancaster Fine Jewelry:
\[
C_1 = 17(2) + 17 = 34 + 17 = 51
\]

- Cost at Bradshaw Jewelers:
\[
C_2 = 15(2) + 21 = 30 + 21 = 51
\]

Both totals agree.

### Final Answer

If Bridgette adds **2** charms to her bracelet, it will cost **$51** at either shop.

So, to fill in the blanks:
If Bridgette adds **2** charms to her bracelet, it will cost **$51** at either shop.