SOLUTION: If 3(4x+5𝛑)=P, in terms of P what is the value of 6(6x+10𝛑)?

After distributing, the above asks:

If 12x+15𝛑=P, in terms of P what is the value of  36x+60𝛑?

Let k and m be such that:

36x + 60𝛑 = kP + m𝛑 
36x + 60𝛑 = k(12x+15𝛑) + m𝛑
36x + 60𝛑 = 12kx + 15k𝛑 + m𝛑

We set coefficients of x equal:

36 = 12k
 3 = k

We set constants equal

60𝛑 = 15k𝛑 + m𝛑
 60 = 15k + m
 60 = 15(3) + m
 60 = 45 + m
 15 = m

so  

36x + 60𝛑 = kP + m𝛑 = 3P + 15𝛑

or

6(6x+10𝛑) = 3P + 15𝛑   <--answer 

Edwin

We are given   = P.


It is the same as   = P.   (1)



Then   = 36x +  = regroup = 36x +  +  =  +  = 


    Now I replace    by  P,  based on (1), and continue the chain of equalities in this way


    = .    Completed.



ANSWER.   Then   = .

    From the expression, which is under the question, I extracted the part, proportional to the given expression.


    Then I replaced this extracted part by the given value (symbol P, in this case).  The remaining addend was simply some constant.