SOLUTION: In what ratio must two sorts of suger, costing $390 and $315 per kg respectively, be mixed in order to produce a mixture worth $345

Let x be the mass of the $390 sugar and y be the mass of $315 sugar.


We want to find the ratio .


Your basic equation is


    390x + 315y = 345*(x+y).     (1)


Why the equation has this form, is absolutely clear, and I will not explain it further.


Since we want to know the ratio  ,  divide equation  (1) by "y" (both sides). You will get


     + 315 = .     (2)


For simplicity, denote   as z; then  equation (2) takes the form


    390*z + 315 = 345*z + 345.


Simplify and find z


    390z - 345z = 345 - 315

    45z = 30

      z =  = .


ANSWER.  The ratio    is  .


         In other words,  2 masses of the $390 sugar should be mixed with  3 masses of the  $315 sugar.


CHECK.    = 345 dollars.   ! Precisely correct !