Question

If n is a positive real number, which of the following is the largest?
3n / (3n + 56)
5n / (5n + 93)
7n / (7n + 131)
Depends on the value of n
3
1
2​

Answer 1

Answer:

(5n + 93)/5n  is Largest

Explanation:

If n is a positive real number, which of the following is the largest?

3n / (3n + 56)

5n / (5n + 93)

7n / (7n + 131)

Lets check their reciprocal

Smallest reciprocal would be largest number

(3n + 56)/3n = 1 + 56/3n

(5n + 93)/5n = 1 + 93/5n

(7n + 131) /7n = 1 + 131/7n

to compare 56/3n , 93/5n & 131/7n

LCM of Denominator 3 , 5 , 7 is 105

56/3n * 105/105  = 1960/105n    

93/5n * 105/105 = 1953/105n

131/7n * 105/105 = 1965/105n

1965 > 1960 > 1953

=> (7n + 131) /7n  >  (3n + 56)/3n > (5n + 93)/5n

=> (7n + 131) /7n < (3n + 56)/3n < (5n + 93)/5n

=> (5n + 93)/5n  is Largest