A total of $\$ 425$ was invested in three different accounts, Account A, Account B and Account C. After one year, the amount in Account A had increased by 5\%, the amount in Account B had increased by 8\%, and the amount in Account C had increased by 10\%. The increase in dollars was the same in each of the three accounts. How much money was originally invested in Account C?
Let $a$ be the amount in dollars initially invested in Account $\mathrm{A}$, let $b$ be the amount in dollars initially invested in Account B, and let $c$ be the amount in dollars initially invested in Account C. The given information leads to the equations $a+b+c=425,0.05 a=0.08 b$, and $0.08 b=0.1 c$. The second and third equations can be solved for $a$ and $b$, respectively, to get $a=\frac{8}{5} b$ and
$b=\frac{5}{4} c$.

Substituting $b=\frac{5}{4} c$ into the equation $a=\frac{8}{5} b$, we get $a=2 c$.

Substituting $a=2 c$ and $b=\frac{5}{4} c$ into the equation $a+b+c=425$ gives

$$
425=a+b+c=2 c+\frac{5}{4} c+c=\frac{17}{4} c
$$

Therefore, the amount in dollars initially invested in Account C is $c=\frac{4}{17} \times 425=100$.

ANSWER: $\$ 100$

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