To solve the given equation from the Babylonian tablet, we first need to clarify the expression. The equation is written as:
\[ x + \frac{x}{7} + \frac{1}{11}(x + \frac{x}{7}) = 60 \]
Let's simplify this step by step.
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Rewrite the equation: \[ x + \frac{x}{7} + \frac{1}{11}(x + \frac{x}{7}) = 60 \]
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Combine terms. Start with the term \( x + \frac{x}{7} \): \[ x + \frac{x}{7} = \frac{7x}{7} + \frac{x}{7} = \frac{8x}{7} \]
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Substitute back into the equation: \[ \frac{8x}{7} + \frac{1}{11} \left(\frac{8x}{7}\right) = 60 \]
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Calculate \( \frac{1}{11} \left(\frac{8x}{7}\right) \): \[ \frac{1 \cdot 8x}{11 \cdot 7} = \frac{8x}{77} \]
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Now the equation is: \[ \frac{8x}{7} + \frac{8x}{77} = 60 \]
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To combine the two fractions, find a common denominator, which is 77: \[ \frac{8x}{7} = \frac{8x \cdot 11}{77} = \frac{88x}{77} \]
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Now combine: \[ \frac{88x}{77} + \frac{8x}{77} = \frac{96x}{77} = 60 \]
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Clear the fraction by multiplying both sides by 77: \[ 96x = 60 \cdot 77 \] \[ 96x = 4620 \]
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Solve for \( x \): \[ x = \frac{4620}{96} \] \[ x = 48.125 \]
So, the solution to the equation is
\( x = 48.125 \).