Question

In $\text{ALFA+BETA+GAMA=DELTA}$, each letter stands for a unique number. Find the value of each letter.

Answer 1

Hint: In this type of question, we should assume the values correctly. Assumption should be exact and accurate. If the assumption is exact and accurate then the answer will be satisfying. The set of values differ based on the set of the assumed values.

Complete step-by-step solution:
From the question we had been given that,
$\text{ALFA+BETA+GAMA=DELTA}$
Let us assume the values of
$A=5$
$L=7$
$F=6$
Now, the value of $\text{ALFA}$ will be equal to,$\text{ALFA=5765}$
Now, let us assume the values of
$\begin{align}
  & B=8 \\
 & E=4 \\
 & T=2 \\
\end{align}$
Now, the value of $BETA$ will be equal to, $BETA=8425$
Now, let us assume the values of
$\begin{align}
  & G=0 \\
 & M=3 \\
\end{align}$
Now, the value of $GAMA$ will be equal to,$GAMA=0535$
Now, let us assume the value of $D=1$
Now the value of \[DELTA\]will be equal to, $DELTA=14725$
Now, we have to check whether $\text{ALFA+BETA+GAMA=DELTA}$ or not.
Therefore, $\text{ALFA+BETA+GAMA=5765+8425+535}$
             $\text{ALFA+BETA+GAMA=14725}$
And before we got the value of $\text{DELTA=14725}$
Therefore $\text{ALFA+BETA+GAMA=DELTA}$
The possible values of each letter would be
$A=5,L=7,F=6,B=8,T=2,G=0,M=3,D=1,E=4$
Now, let us assume another set of values.
Let us assume the values of
$\begin{align}
  & \text{A=5} \\
 & \text{L=7} \\
 & \text{F=6} \\
\end{align}$
Now, the value of $\text{ALFA}$ will be equal to,
$\text{ALFA=5765}$
Now, let us assume the values of
$\begin{align}
  & \text{B=0} \\
 & \text{E=4} \\
 & \text{T=2} \\
\end{align}$
Now, the value of $\text{BETA}$ will be equal to,
$\text{BETA=425}$
Now, let us assume the values of
$\begin{align}
  & \text{G=8} \\
 & \text{M=3} \\
\end{align}$
Now, the value of $\text{GAMA}$ will be equal to,
$\text{GAMA=8535}$
Now, let us assume the value of $D=1$
Now, the value of $DELTA$ will be equal to,
$DELTA=14725$
Now, we have to check whether $\text{ALFA+BETA+GAMA=DELTA}$ or not,
$\begin{align}
  & \text{ALFA+BETA+GAMA=5765+425+8535} \\
 & \Rightarrow \text{ALFA+BETA+GAMA=14725} \\
\end{align}$
Hence verified,
The possible set of values for $\text{ALFA+BETA+GAMA=DELTA}$ are ,
($A=5,L=7,F=6,B=8,T=2,G=0,M=3,D=1,E=4$)
($A=5,L=7,F=6,B=0,T=2,G=8,M=3,D=1,E=4$)

Note: In this type of question we should have to assume the values exactly and accurately. We should assume the values and verify the values assumed are whether correct or not. We should verify the set of values which are assumed to be satisfying or not. For questions of this type the set of values may differ but can satisfy the given condition.