+0  
 
0
1
1
avatar+701 

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by 1. He then multiplies all his fractions together. He has 3 fractions, and their product equals 10. What is the value of the first fraction he wrote?

 Jun 26, 2024
 #1
avatar+129725 
+1

(n + 2) / n   *  (n + 3)/ ( n + 1) * ( n + 4) / (n + 2)  = 10     simplify

 

1/n * (n + 3) / (n + 1) * (n + 4) =  10

 

(n + 3) (n + 4)  =  10 ( n)(n + 1)

 

n^2 + 7n + 12 = 10n^2 + 10n

 

9n^2 + 3n - 12 = 0 

 

3n^2 + n - 4  =  0

 

(3n + 4) (n -1 )  = 0

 

n = 1      n  =  -4/3

 

Only n = 1  is good

 

Value of  first fraction  =  3 / 1  =  3

 

cool cool cool

 Jun 26, 2024

1 Online Users