((30×70) + (56×90) + (59×110) + (79×135) + (23×160)​)/247

asked by guest
on Oct 21, 2024 at 4:52 am



You asked:

Evaluate the expression: \(\frac{30 \cdot 70 + 56 \cdot 90 + 59 \cdot 110 + 79 \cdot 135 + 23 \cdot 160}{247}\)

MathBot Answer:

\[\frac{30 \cdot 70 + 56 \cdot 90 + 59 \cdot 110 + 79 \cdot 135 + 23 \cdot 160}{247} = \frac{27975}{247} = 113.\overline{259109311740890688}\]

\[\begin{aligned}\frac{30 \cdot 70 + 56 \cdot 90 + 59 \cdot 110 + 79 \cdot 135 + 23 \cdot 160}{247}& = \left(30 \cdot 70 + 56 \cdot 90 + 59 \cdot 110 + 79 \cdot 135 + 23 \cdot 160\right) \cdot \frac{1}{247}\\& = \left(2100 + 56 \cdot 90 + 59 \cdot 110 + 79 \cdot 135 + 23 \cdot 160\right) \cdot \frac{1}{247}\\& = \left(2100 + 5040 + 59 \cdot 110 + 79 \cdot 135 + 23 \cdot 160\right) \cdot \frac{1}{247}\\& = \left(2100 + 5040 + 6490 + 79 \cdot 135 + 23 \cdot 160\right) \cdot \frac{1}{247}\\& = \left(2100 + 5040 + 6490 + 10665 + 23 \cdot 160\right) \cdot \frac{1}{247}\\& = \left(2100 + 5040 + 6490 + 10665 + 3680\right) \cdot \frac{1}{247}\\& = \left(7140 + 6490 + 10665 + 3680\right) \cdot \frac{1}{247}\\& = \left(13630 + 10665 + 3680\right) \cdot \frac{1}{247}\\& = \left(24295 + 3680\right) \cdot \frac{1}{247}\\& = \frac{27975}{247}\end{aligned}\]

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