Walt made an extra $5000 last year from a part-time job. He invested part of the money at 8% and arrest at 10%. He made a total of $480 and interest how much was invested at 10%.

To solve this problem, let's use the method of setting up and solving equations. Let:

- $ x $ be the amount of money invested at 8%.
- $ y $ be the amount of money invested at 10%.

We know the following:

1. Walt made a total of $5000 from his part-time job, so the sum of the investments is:
   \[
   x + y = 5000
   \]

2. The total interest earned from both investments is $480. The interest earned from the 8% investment is $ 0.08x $, and the interest earned from the 10% investment is $ 0.10y $. Therefore, the equation for the total interest is:
   \[
   0.08x + 0.10y = 480
   \]

Now, let's solve these equations step by step.

### Step 1: Solve the first equation for $ x $:
\[
x = 5000 - y
\]

### Step 2: Substitute this expression for $ x $ into the second equation:
\[
0.08(5000 - y) + 0.10y = 480
\]

### Step 3: Distribute and simplify:
\[
400 - 0.08y + 0.10y = 480
\]
\[
0.02y = 480 - 400
\]
\[
0.02y = 80
\]

### Step 4: Solve for $ y $:
\[
y = \frac{80}{0.02} = 4000
\]

So, Walt invested **$4000** at 10%.

### Verification:
- $ x = 5000 - 4000 = 1000 $ was invested at 8%.
- Interest from 8% investment: $ 0.08 \times 1000 = 80 $.
- Interest from 10% investment: $ 0.10 \times 4000 = 400 $.
- Total interest: $ 80 + 400 = 480 $, which matches the given total interest.

This confirms the solution is correct.

Would you like further details or have any questions?

---

1. How do you calculate the interest from investments?
2. What are the steps to solving linear equations?
3. How would the answer change if the interest rates were different?
4. What would happen if Walt had invested all the money at 8%?
5. How do you interpret and set up equations from word problems?

**Tip:** Always check your solution by substituting the values back into the original problem to ensure they satisfy all given conditions.

Learn how to calculate interest from investments using a part-time job problem solved step-by-step. Walt earned $5000 last year and invested part at 8% and the rest at 10%, totaling $480 in interest. Discover the solution and verify the calculations.

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