Remaining

Mum baked buns for dinner. Dad ate 1/3 of them. Then George came and ate a quarter of the remaining buns. After George, Martin came and ate a third of what was left. Annie ate half of the remaining buns, and Mum was left with four buns. How many buns did Mum bake, and how many did each family member eat?

Final Answer:

O =  24
o =  8
j =  4
m =  4
a =  4
m₂ =  4

Step-by-step explanation:

$$\begin{gathered} A-A/2=4 \\ A/2=4 \\ A=2\cdot 4=8 \\ M-M/3=A \\ \frac{2}{3}M=A \\ M=\frac{3}{2}\cdot A=\frac{3}{2}\cdot 8=\frac{3\cdot 8}{2}=\frac{24}{2}=12 \\ J-J/4=M \\ \frac{3}{4}J=M \\ J=\frac{4}{3}\cdot M=\frac{4}{3}\cdot 12=\frac{4\cdot 12}{3}=\frac{48}{3}=16 \\ O-O/3=J \\ \frac{2}{3}O=J \\ O=\frac{3}{2}\cdot J=\frac{3}{2}\cdot 16=\frac{3\cdot 16}{2}=\frac{48}{2}=24 \end{gathered}$$

$o=O/3=24/3=8$

$j=J/4=16/4=4$

$m=M/3=12/3=4$

$a=A/2=8/2=4$

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