Question

If p,q,r and s are four different positive integers selected from 1 to 50, then find the highest possible value of
$(p\: + q) + (r + s ) \div (p \: + q) + (r - s ) .$
35 points
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Answer 1

Answer:

1.94

Step-by-step explanation:

Max of (p+q)+(r+s) ÷(p+q)+(r- s) = (50+49)+(48+47) ÷(50+49)+(48- 47) = 1.94

Answer 2

Answer:

I= (p+q)+(r+s) / (p+q)+(r-s)

0<p,q,r,s≤50

⇒ (p+q+r)+s / (p+q+r)-s

⇒ (p+q+r−s) +2s / (p+q+r)−s

I⇒1+ 2s/(p+q+r)-2s

I to be maximum

(p+q+r)−s=1 and s should be maximum

∴ if. (p+q+r) = 50 => s =49

=> I = 1 + 2*49/(50-49)

=> I = 1 + 98

=> I = 99