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Algebra Difficulty 5.1 AIME, harder Find the answer

Lily is 90 cm90 \mathrm{~cm} tall. If Anika is 43\frac{4}{3} of the height of Lily, and Sadaf is 54\frac{5}{4} of the height of Anika, how tall is Sadaf?

Pick one

Solution

Solution 1

Since Lily is 90 cm90 \mathrm{~cm} tall, Anika is 43\frac{4}{3} as tall as Lily, and Sadaf is 54\frac{5}{4} as tall as Anika, then Sadaf is 54×43×90=53×90=4503=150 cm\frac{5}{4} \times \frac{4}{3} \times 90=\frac{5}{3} \times 90=\frac{450}{3}=150 \mathrm{~cm} tall.

## Solution 2

Since Lily is 90 cm90 \mathrm{~cm} tall and Anika is 43\frac{4}{3} of her height, then Anika is 43×90=3603=120 cm\frac{4}{3} \times 90=\frac{360}{3}=120 \mathrm{~cm} tall. Since Anika is 120 cm120 \mathrm{~cm} tall and Sadaf is 54\frac{5}{4} of her height, then Sadaf is 54×120=6004=150 cm\frac{5}{4} \times 120=\frac{600}{4}=150 \mathrm{~cm} tall.

ANswer: (E)

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