Question

the value of x in the preparation 9 : 5 : :36 : x - 3 is

Answer 1

 9/5=36/x-3 

One solution was found :

                   x = 15/2 = 7.500

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     9/5-(36/x-3)=0 

Step by step solution :

Step  1  :

36 Simplify —— x

Equation at the end of step  1  :

9 36 — - (—— - 3) = 0 5 x

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction 

Rewrite the whole as a fraction using  x  as the denominator :

3 3 • x 3 = — = ————— 1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 2.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

36 - (3 • x) 36 - 3x ———————————— = ——————— x x

Equation at the end of step  2  :

9 (36 - 3x) — - ————————— = 0 5 x

Step  3  :

9 Simplify — 5

Equation at the end of step  3  :

9 (36 - 3x) — - ————————— = 0 5 x

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   36 - 3x  =   -3 • (x - 12) 

Calculating the Least Common Multiple :

 5.2    Find the Least Common Multiple 

      The left denominator is :       5 

      The right denominator is :       x 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 5101 Product of all 
 Prime Factors 515

Answer 2

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