Remaining

Aladár promised his mother that he would wash the plates. In order not to get 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 remaining three plates. How many plates did he wash at which stage?

Final Answer:

a =  63
b =  42
c =  144
d =  3

Step-by-step explanation:

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

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

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

$d=3$

Try another example