Remaining

Aladár promised his mother that he would wash the dishes. To avoid getting too tired, he divided the work into four stages. First, he washed one quarter of all the plates. After a short rest, he washed one sixth of all the plates. After a long rest, he washed four sevenths of the remaining plates, and finally washed the last three plates. How many plates did he wash at each stage?

Final Answer:

a =  63
b =  42
c =  144
d =  3

Step-by-step explanation:

$$\begin{gathered} n/4+n/6+4/7\cdot n+3=n \\ n=252 \\ a=n/4=252/4=63 \end{gathered}$$

$b=n/6=252/6=42$

$c=4/7\cdot n=4/7\cdot 252=144$

$d=3$

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