Remaining

Mom baked buns for dinner. Dad ate 1/3 of them. Then Jurko came and ate a quarter of the remaining buns. After Jurko came to Martin, who ate a third of the remaining buns. Anka ate half of the remaining buns and Mom was left with four buns. How many buns did mom bake and how many did each family member eat?

Correct answer:

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

Step-by-step explanation:

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

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

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

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

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

Try another example