AMC 8 2020 Problem 16 | Line Problem

Try this beautiful Problem based on line from AMC 8 2020.

Lines Problem - AMC 8 2020 Problem 16

Each of the points $A, B, C, D, E$, and $F$ in the figure below represents a different digit from 1 to 6 . Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is 47 . What is the digit represented by $B$ ?

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Key Concepts

Lines

Combination

Digit Find

Suggested Book | Source | Answer

Source of the Problem

Answer

AMC 8 2020 Problem 16

5

Try with Hints

Hint 1

Hint 2

Hint 3

Try to find the sumes alongs lines

\begin{aligned}
&A+B+C \
&A+E+F \
&C+D+E \
&B+D \
&B+F
\end{aligned}

Adding The sums all together, we will have $2 A+3 B+2 C+2 D+2 E+2 F=47$, i.e. $2(A+B+C+D+E+F)+B=47$

So we will have $42+B=47$, now we need solve this equation for B.

Lines Problem - AMC 8 2020 Problem 16

Each of the points $A, B, C, D, E$, and $F$ in the figure below represents a different digit from 1 to 6 . Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is 47 . What is the digit represented by $B$ ?