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avatar+1351 

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?

 Mar 22, 2024
 #1
avatar+128794 
+1

(x + 2) / x  *  ( x + 3) / (x + 1)  *  ( x + 4)  / (x + 2)   = 10

 

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

 

(x + 3) ( x + 4)  = 10 (x) (x + 1)

 

x^2  + 7x + 12  = 10x^2 + 10x

 

9x^2 + 3x - 12  = 0

 

3x^2  + x  - 4  =  0

 

(3x + 4) ( x - 1)  = 0

 

(x - 1)  = 0

 

x = 1

 

First fraction  = (1 + 2) / 1  =  3 / 1

 

 

cool cool cool

 Mar 23, 2024

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