A gadget enthusiast Nick decided to buy some electronic accessories at a tech store. He aimed to buy twice as many Bluetooth tracker as USB cables and at least one more USB cables than wireless chargers. USB cables cost three times as much as wireless chargers, and wireless chargers are priced at half the cost of Bluetooth trackers. Each wireless charger costs €1, and Nick's total bill came to €47.

The total number of gadgets purchased by Nick is

We can solve this problem by using variables and forming equations based on the given information.

Let:
- \( x \) be the number of wireless chargers,
- \( y \) be the number of USB cables,
- \( z \) be the number of Bluetooth trackers.

### Step 1: Formulating the equations

From the problem, we are given the following relationships:

1. **USB cables are at least one more than wireless chargers**:
   \[
   y = x + 1
   \]
   
2. **Nick aimed to buy twice as many Bluetooth trackers as USB cables**:
   \[
   z = 2y
   \]
   
3. **The price relationships**:
   - Each wireless charger costs €1.
   - The price of each USB cable is three times the cost of a wireless charger, so each USB cable costs €3.
   - The price of each Bluetooth tracker is double the cost of a wireless charger, so each Bluetooth tracker costs €2.

4. **Total cost**: Nick's total bill came to €47.

The total cost equation is:
\[
1x + 3y + 2z = 47
\]

### Step 2: Substituting values and solving

From equation \( z = 2y \), substitute into the total cost equation:
\[
x + 3y + 2(2y) = 47
\]
Simplify:
\[
x + 3y + 4y = 47
\]
\[
x + 7y = 47
\]

Now, substitute \( y = x + 1 \) into the equation:
\[
x + 7(x + 1) = 47
\]
Expand:
\[
x + 7x + 7 = 47
\]
\[
8x + 7 = 47
\]
Solve for \( x \):
\[
8x = 40
\]
\[
x = 5
\]

### Step 3: Finding the number of USB cables and Bluetooth trackers

Now that we know \( x = 5 \), substitute this into \( y = x + 1 \):
\[
y = 5 + 1 = 6
\]

Then, substitute \( y = 6 \) into \( z = 2y \):
\[
z = 2(6) = 12
\]

### Step 4: Total number of gadgets purchased

The total number of gadgets is:
\[
x + y + z = 5 + 6 + 12 = 23
\]

Thus, Nick purchased **23 gadgets**.

---

Would you like more details on any part of the solution or have any questions?

Here are some related questions to further explore:

1. What if the price of wireless chargers increased to €2?
2. How would Nick's total cost change if he bought three times as many Bluetooth trackers as USB cables?
3. What would be the number of gadgets if Nick purchased one less Bluetooth tracker?
4. How would the number of gadgets change if USB cables cost four times as much as wireless chargers?
5. What if Nick had a budget of €60, how many gadgets could he buy?

**Tip:** When solving word problems, always break down relationships between variables first and gradually substitute them to simplify the problem.

A gadget enthusiast Nick decided to buy some electronic accessories at a tech store. He aimed to buy twice as many Bluetooth trackers as USB cables and at least one more USB cable than wireless chargers. USB cables cost three times as much as wireless chargers, and wireless chargers are priced at half the cost of Bluetooth trackers. Each wireless charger costs €1, and Nick's total bill came to €47. The total number of gadgets purchased by Nick is?

Explore how to solve a real-world algebraic problem involving gadgets and pricing. Nick's tech store purchase includes Bluetooth trackers, USB cables, and wireless chargers. Learn how to use systems of equations to determine the number of gadgets purchased with a total bill of €47. Suitable for Grades 8-10.

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