To solve the equation \( 3(11 - p) + 2.5p = 31p \), let's start by simplifying the left side of the equation.
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Distribute the 3 into the parentheses: \[ 3 \cdot 11 - 3p = 33 - 3p \]
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Now, substitute this back into the equation: \[ 33 - 3p + 2.5p = 31p \]
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Combine like terms on the left side: \[ 33 - 0.5p = 31p \]
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Next, get all terms involving \( p \) on one side and the constants on the other. Add \( 0.5p \) to both sides: \[ 33 = 31p + 0.5p \] \[ 33 = 31.5p \]
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Now, solve for \( p \) by dividing both sides by 31.5: \[ p = \frac{33}{31.5} \]
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To simplify, \[ p \approx 1.047619 \]
Therefore, the approximate solution is: \[ p \approx 1.05 \]
If you'd like, I can convert it to a fraction: \[ p = \frac{11}{10.5} \text{ which simplifies to } \frac{22}{21} \text{ or } 1.047619... \]
So, the final solution is: \[ p \approx 1.05 \] or \( p = \frac{22}{21} \).