Cakes

A few cakes were in the bowl. Jane ate one-third of them, and Dana ate a quarter of the remaining cakes.

a) What part (of the original number of cakes) Dana ate?
b) How many cakes could be (initially) on the bowl?

Final Answer:

a =  1/6
b =  6

Step-by-step explanation:

$$\begin{gathered} z_1=1-\frac{1}{3}=\frac{1\cdot 3}{3}-\frac{1}{3}=\frac{3}{3}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}\doteq 0.6667 \\ a=z_1/4=\frac{2}{3}/4=\frac{2}{3\cdot 4}=\frac{2}{12}=\frac{1}{6}=0.1667 \end{gathered}$$

$b=1/a=1/\frac{1}{6}=1:\frac{1}{6}=1\cdot \frac{6}{1}=\frac{1\cdot 6}{1}=\frac{6}{1}=6$

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