Inequality word problem

Algebra Level 2

The age of son is 1 4 \frac 14 times the age of his father. His mother is 8 years younger than father. The sum of the ages of all of them is not greater than 91. If the age of mother is not greater than y y , find y y


The answer is 36.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Joshua Lowrance
Aug 30, 2018

f a t h e r = f ; m o t h e r = m ; s o n = s father = f; mother = m; son = s

f = m + 8 ; s = 1 4 ( f ) = 1 4 ( m + 8 ) = 1 4 m + 2 f = m + 8; s = \frac{1}{4}(f) = \frac{1}{4}(m + 8) = \frac{1}{4}m + 2

91 ≥ s + f + m 91 ≥ 1 4 m + 2 + m + 8 + m 91 ≥ 9 4 m + 10 81 ≥ 9 4 m 36 ≥ m 91 \geq s + f + m \\ 91 \geq \frac{1}{4}m + 2 + m + 8 + m \\\\ 91 \geq \frac{9}{4}m + 10 \\\\\\ 81 \geq \frac{9}{4}m \\\\\\\\ 36 \geq m

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