Three 233

Three adults and one child want to share the remaining 4/5 of a pie between them. They agree the child gets 3/10 of that amount, while the adults share what's left after the child is served. How much of a whole pie do the adults get? Report your answer as a fraction.

Correct answer:

a =  19/75

Step-by-step explanation:

$$\begin{gathered} 3a+1b \\ C=\frac{3}{10}\cdot \frac{4}{5}=\frac{3\cdot 4}{10\cdot 5}=\frac{12}{50}=\frac{6}{25}=0.24 \\ A=1-C=1-\frac{6}{25}=\frac{1\cdot 25}{25}-\frac{6}{25}=\frac{25}{25}-\frac{6}{25}=\frac{25-6}{25}=\frac{19}{25}=0.76 \\ a=A/3=\frac{19}{25}/3=\frac{19}{25\cdot 3}=\frac{19}{75}=0.2533 \end{gathered}$$

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