[(952*8.17 + 4000*5.91)/(952 + 4000)]

asked by guest
on Oct 22, 2024 at 8:03 am



You asked:

Evaluate the expression: \(\frac{952 \cdot 8.17 + 4000 \cdot 5.91}{952 + 4000}\)

MathBot Answer:

\[\frac{952 \cdot 8.17 + 4000 \cdot 5.91}{952 + 4000} = \frac{392723}{61900} \approx 6.34447495961227786752827140549273\]

\[\begin{aligned}\frac{952 \cdot 8.17 + 4000 \cdot 5.91}{952 + 4000}& = \left(952 \cdot \left(8 + \frac{17}{100}\right) + 4000 \cdot \left(5 + \frac{91}{100}\right)\right) \cdot \frac{1}{952 + 4000}\\& = \left(952 \cdot \frac{817}{100} + 4000 \cdot \left(5 + \frac{91}{100}\right)\right) \cdot \frac{1}{952 + 4000}\\& = \left(\frac{194446}{25} + 4000 \cdot \left(5 + \frac{91}{100}\right)\right) \cdot \frac{1}{952 + 4000}\\& = \left(\frac{194446}{25} + 4000 \cdot \frac{591}{100}\right) \cdot \frac{1}{952 + 4000}\\& = \left(\frac{194446}{25} + 23640\right) \cdot \frac{1}{952 + 4000}\\& = \frac{785446}{25} \cdot \frac{1}{952 + 4000}\\& = \frac{785446}{25} \cdot \frac{1}{4952}\\& = \frac{392723}{61900}\end{aligned}\]

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