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Answer :
Let the three consecutive integers be x, x + 1 and x + 2.
As per the condition given, we have
2x + 3(x + 1) + 4(x + 2) = 74
\(\Rightarrow\) 2x + 3x + 3 + 4x + 8 = 74
\(\Rightarrow\) 9x + 11 = 74
\(\Rightarrow\) 9x = 74 – 11 (transposing 11 to RHS)
\(\Rightarrow\) 9x = 63
\(\Rightarrow\) x = 63 ÷ 9 (transposing 9 to RHS)
\(\Rightarrow\) x = 7
Thus, the required numbers are 7, 7 + 1 = 8 and 7 + 2 = 9, i.e., 7, 8 and 9.