Finding the sum of coefficients of the reaction What is the sum of the coefficients $(a + b + c)$ in the following reaction?
$$\ce{x Zn + y HNO3} -&gt; {a Zn(NO3)2 + b H2O + c NH4NO3}$$

Here if the equation is balanced we get 1 mol of $\ce{Zn}$ and 4 mol of $\ce{HNO3}$. As  $x + y = a + b + c$ we get sum of coefficients $a + b + c = 5$. According to me, this is the correct answer, but in the actual answer key the answer is 8.
I may be wrong, but can someone help me clarify the right answer?
Linear equations aside, note that this is a redox reaction and you can use half-reactions method as well (BTW the reaction looks fine to me):

$$\ce{$x$ \overset{0}{Zn} + y H\overset{+5}{N}O3 -&gt; $a$ \overset{+2}{Zn}(NO3)2 + b H2O + $c$ \overset{-3}{N}H4NO3}$$

$$
\begin{align}
\ce{\overset{+5}{N} + 8 e- &amp;→ \overset{-3}{N}} \tag{red}\\
\ce{\overset{0}{Zn} &amp;→ \overset{+2}{Zn} + 2 e-} &amp;|\cdot 4 \tag{ox}\\
\hline
\ce{4 \overset{0}{Zn} + \overset{+5}{N} &amp;→ 4 \overset{+2}{Zn} + \overset{-3}{N}} \tag{redox}
\end{align}
$$

So that the complete balanced equation is

$$\ce{4 Zn + 10 HNO3 -&gt; 4 Zn(NO3)2 + 3 H2O + NH4NO3}$$

leaving $a = 4$, $b = 3$, $c = 1$ and the sum $a + b + c = 4 + 3 + 1 = 8$.