Improper fraction with inequality

Algebra Level 3

Given the improper fraction 3 a + 16 5 a − 4 \dfrac{3a+16}{5a-4} , and a a is the largest possible value. What is the value of a a ?


The answer is 10.

Luiz Claudio by Luiz Claudio , 19, Brazil

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1 solution

Vedant Saini
Feb 25, 2019

The question implies 3 a + 16 ≥ 5 a − 4 3a + 16 \geq 5a - 4

⟹ 20 ≥ 2 a \implies 20 \geq 2a

⟹ 10 ≥ a \implies 10 \geq a

Thus maximum value of a a is 10 10

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