Leaves Fall Four Days

In the park, one-third of all the leaves on the trees fell on the first day. On the second day, a quarter of what remained on the branches fell, and a third of the remaining leaves on the third day. Half of the leaves were blown off the trees on the fourth day, leaving 422 on the branches. How many leaves fell in these four days?

Final Answer:

n =  1266

Step-by-step explanation:

$$\begin{gathered} d_1=1/3=\frac{1}{3}\doteq 0.3333 \\ {d}_2=1/4\cdot (1-d_1)=1/4\cdot (1-0.3333)=\frac{1}{6}\doteq 0.1667 \\ {d}_3=1/3\cdot (1-d_2-d_1)=1/3\cdot (1-0.1667-0.3333)=\frac{1}{6}\doteq 0.1667 \\ n/3+n/6+n/6+422=n \\ 0.333333n=422 \\ \frac{1}{3}n=422 \\ n=1266 \end{gathered}$$

n/3 + n/6 + n/6 + 422 = n

2n = 2532


n = 2532/2 = 1266

n = 1266

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