To solve the equation \( \frac{3}{8}y - 2\frac{7}{8} = 13 \), we can follow these steps:
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Convert mixed number to improper fraction: \[ 2\frac{7}{8} = \frac{16}{8} + \frac{7}{8} = \frac{23}{8} \]
So the equation becomes: \[ \frac{3}{8}y - \frac{23}{8} = 13 \]
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Add \(\frac{23}{8}\) to both sides: \[ \frac{3}{8}y = 13 + \frac{23}{8} \]
To add these, convert 13 into a fraction with a denominator of 8: \[ 13 = \frac{104}{8} \] Thus, \[ 13 + \frac{23}{8} = \frac{104}{8} + \frac{23}{8} = \frac{127}{8} \]
Now, the equation is: \[ \frac{3}{8}y = \frac{127}{8} \]
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Multiply both sides by the reciprocal of \(\frac{3}{8}\) (which is \(\frac{8}{3}\)): \[ y = \frac{127}{8} \cdot \frac{8}{3} = \frac{127 \cdot 8}{8 \cdot 3} = \frac{127}{3} \]
So the solution to the equation is: \[ y = \frac{127}{3} \]
You can also convert this to a decimal or mixed number if needed: \[ y \approx 42.33 \quad \text{or} \quad 42 \frac{1}{3} \]