Does the calculation \( 78,604-3514=74,090 \) have an error based on casting out nines? A. The calculation checks using casting out nines. The remainder is B. Casting out nines shows there is an error. The given answer has a remainder of \( \square \), but casting out nines gives a remainder of \( \square \). The correct answer is \( \square \).

1. **Calculate the digital root (casting out nines) of the minuend and subtrahend:** - For \(78{,}604\): Sum of digits: \[ 7+8+6+0+4=25,\quad 2+5=7. \] So, \(78{,}604 \equiv 7 \pmod{9}\). - For \(3{,}514\): Sum of digits: \[ 3+5+1+4=13,\quad 1+3=4. \] So, \(3{,}514 \equiv 4 \pmod{9}\). 2. **Compute the expected digital root for the correct difference:** Subtraction remainder should be: \[ 7-4=3 \quad (\text{mod }9). \] Thus, the correct difference should be congruent to \(3 \pmod{9}\). 3. **Analyze the given answer \(74{,}090\):** Sum of digits: \[ 7+4+0+9+0=20,\quad 2+0=2. \] Hence, \(74{,}090 \equiv 2 \pmod{9}\), which does not match the expected remainder of \(3\). 4. **Conclusion:** \(\boxed{\text{B. Casting out nines shows there is an error. The given answer has a remainder of }2,\text{ but casting out nines gives a remainder of }3. \text{ The correct answer is }75{,}090.}\)