There-are-three-positive-integers-a-b-and-c-such-that-their-average-is-35-and-a-b-c-If-the-median-is-a-18-then-find-the-minimum-possible-value-of-c-1-41-2-42-

Question Number 206675 by BaliramKumar last updated on 22/Apr/24

$$ \\ $$There are three positive integers a, b, and c such that
their average is 35 and a ≤ b ≤ c. If the median is
(a + 18), then find the minimum possible value of c.
(1) 41. (2) 42. (3) 39. (4) 40

Answered by mr W last updated on 22/Apr/24

$${a}>\mathrm{0} \\ $$$${a}+{b}+{c}=\mathrm{3}×\mathrm{35}=\mathrm{105} \\ $$$${b}={a}+\mathrm{18}\leqslant{c} \\ $$$${c}=\mathrm{105}−{a}−{a}−\mathrm{18}=\mathrm{87}−\mathrm{2}{a}\geqslant{a}+\mathrm{18} \\ $$$$\Rightarrow{a}\leqslant\mathrm{23} \\ $$$${c}=\mathrm{87}−\mathrm{2}{a}\geqslant\mathrm{87}−\mathrm{2}×\mathrm{23}=\mathrm{41}\:\checkmark \\ $$$$\Rightarrow{answer}\:\left(\mathrm{1}\right) \\ $$

Commented by BaliramKumar last updated on 22/Apr/24

$$\mathrm{thanks} \\ $$

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