To simplify the expression \(1.3w + 6.2 + 8.5 + 5.7 + 7.7\), we will first combine the constant terms:
\[ 6.2 + 8.5 + 5.7 + 7.7 \]
Calculating the sum step by step:
\[ 6.2 + 8.5 = 14.7 \] \[ 14.7 + 5.7 = 20.4 \] \[ 20.4 + 7.7 = 28.1 \]
Now, substituting this back into the expression gives us:
\[ 1.3w + 28.1 \]
Thus, the simplified expression is:
\[ \boxed{1.3w + 28.1} \]
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