[(952*8.17 + 5000*5.91)/(952 + 5000)]

asked by guest
on Oct 22, 2024 at 8:04 am



You asked:

Evaluate the expression: \(\frac{952 \cdot 8.17 + 5000 \cdot 5.91}{952 + 5000}\)

MathBot Answer:

\[\frac{952 \cdot 8.17 + 5000 \cdot 5.91}{952 + 5000} = \frac{233299}{37200} = 6.2714\overline{784946236559139}\]

\[\begin{aligned}\frac{952 \cdot 8.17 + 5000 \cdot 5.91}{952 + 5000}& = \left(952 \cdot \left(8 + \frac{17}{100}\right) + 5000 \cdot \left(5 + \frac{91}{100}\right)\right) \cdot \frac{1}{952 + 5000}\\& = \left(952 \cdot \frac{817}{100} + 5000 \cdot \left(5 + \frac{91}{100}\right)\right) \cdot \frac{1}{952 + 5000}\\& = \left(\frac{194446}{25} + 5000 \cdot \left(5 + \frac{91}{100}\right)\right) \cdot \frac{1}{952 + 5000}\\& = \left(\frac{194446}{25} + 5000 \cdot \frac{591}{100}\right) \cdot \frac{1}{952 + 5000}\\& = \left(\frac{194446}{25} + 29550\right) \cdot \frac{1}{952 + 5000}\\& = \frac{933196}{25} \cdot \frac{1}{952 + 5000}\\& = \frac{933196}{25} \cdot \frac{1}{5952}\\& = \frac{233299}{37200}\end{aligned}\]

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