In the following equations, the letters $a, b$ and $c$ represent different numbers.

$$
\begin{aligned}
& 1^{3}=1 \\
& a^{3}=1+7 \\
& 3^{3}=1+7+b \\
& 4^{3}=1+7+c
\end{aligned}
$$

The numerical value of $a+b+c$ is
(A) 58
(B) 110
(C) 75
(D) 77
(E) 79
In the following equations, the letters $a, b$ and $c$ represent different numbers.

$$
\begin{aligned}
& 1^{3}=1 \\
& a^{3}=1+7 \\
& 3^{3}=1+7+b \\
& 4^{3}=1+7+c
\end{aligned}
$$

The numerical value of $a+b+c$ is
(A) 58
(B) 110
(C) 75
(D) 77
(E) 79

## Solution

Since $2^{3}=8=1+7$, then $a=2$.

Since $3^{3}=27$, then $27=8+b$ or $b=19$.

Since $4^{3}=64$, then $64=8+c$ or $c=56$.

Thus, $a+b+c=2+19+56=77$.

ANSWER: (D)