A can of nuts has almonds and cashews in a ratio of \(x:y.\) If there are \(z\) almonds in the can, which of the followi

[VJesus12]

A can of nuts has almonds and cashews in a ratio of \(x:y.\) If there are \(z\) almonds in the can, which of the following represents the number of cashews?

A. \(y(x + z)\)
B. \(y(z - y)\)
C. \(\dfrac{xy}{z}\)
D. \(\dfrac{yz}{x}\)
E. \(x\)

Answer: D

Source: Princeton Review

[deloitte247]

Ratio of almonds to cashew => x:y => x/y
If total almonds = z
Let total nuts = a
$$\frac{Almonds}{Cashew}=\frac{x\cdot a}{y\cdot a}$$
Almonds = xa
i.e z = xa
and a = z/x
Cashew = ya, where a = z/x
$$Therefore,\ cashew\ =\ y\ \cdot\ \frac{z}{x}=\frac{yz}{x}$$

Answer = option D