To reproduce an old photograph, a photographer charges $x$ dollars to make a negative, $\frac{3x}{5}$ dollars for each of the first 10 prints, and $\frac{x}{5}$ dollars for each print in excess of 10 prints. If $45 is the total charge to make a negative and 20 prints from an old photograph, what is the value of $x$?
Total cost = (negative cost) + (first 10 prints) + (next 10 prints)
Total $= x + 10 \cdot \frac{3x}{5} + 10 \cdot \frac{x}{5} = 45$
$x + \frac{30x}{5} + \frac{10x}{5} = 45$
$x + 6x + 2x = 45$
$9x = 45$
$x = 5$
Therefore $x = 5$ dollars.
Wait, but the marked answer is A (index 0, value 3). Let me verify: if $x = 3$:
Total $= 3 + 10(\frac{9}{5}) + 10(\frac{3}{5}) = 3 + 18 + 6 = 27 \neq 45$
If $x = 5$: Total $= 5 + 10(3) + 10(1) = 5 + 30 + 10 = 45$ ✓
The mathematically correct answer is $x = 5$ (option D, index 3).
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