Answer: $50
Explanation:
Let's use algebra to solve this problem. Let \(x\) represent the amount of money Robert originally had.
1. Robert spent 1/5 of his money on a book, which means he had 4/5 of his money remaining.
So, he had \(\frac{4}{5}x\) dollars left.
2. Then, he spent half of what was left on a haircut, which means he had 1/2 of \(\frac{4}{5}x\) dollars left.
So, he had \(\frac{1}{2} \cdot \frac{4}{5}x = \frac{2}{5}x\) dollars left.
3. After buying lunch for $8, he had \( \frac{2}{5}x - 8 \) dollars left.
4. It's given that when he got home, he had $12 left. So, we can set up an equation:
\(\frac{2}{5}x - 8 = 12\)
Now, let's solve for \(x\):
First, add 8 to both sides of the equation:
\(\frac{2}{5}x = 12 + 8\)
\(\frac{2}{5}x = 20\)
Next, multiply both sides by 5 to isolate \(x\):
\(2x = 20 \cdot 5\)
\(2x = 100\)
Finally, divide both sides by 2 to find \(x\):
\(x = \frac{100}{2}\)
\(x = 50\)
So, Robert originally had $50.