Question 1208072
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the mass of a bag of red star sugar is 20% greater than the mass of a bag of blue star sugar. 
However, a bag of red star sugar costs 50% more than a bag of blue star sugar. 
for the same mass, red star sugar costs how much percent more than blue star sugar?
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<pre>
Let m be the mass of the blue star sugar in a bag, in which they sell it (in kilograms).


Then the mass of the red star sugar in a bag, in which they sell it is 1.2m kilograms, 
according to the problem's description.


Let x be the price of one kilogram of the blue star sugar.

Let y be the price of one kilogram of the red  star sugar.



      They want you find the ratio  {{{y/x}}}.



Since a bag of red star sugar costs 50% more than a bag of blue star sugar 
we can write this equation

    x*m*1.5 = y*(1.2*m).    (1)


In this equation, left side  is the cost of one bag of the blue star sugar increased by 50%; 
                  right side is the cost of one bag of the red  star sugar.


From equation (1),  the ratio  {{{y/x}}}  is

    {{{y/x}}} = {{{(m*1.5)/(1.2*m)}}} = reduce m in the numerator and denominator = {{{1.5/(1.2)}}} = 1.25.



            Thus, the price of one kilo of the red star sugar 
    is 1.25, or 125% of the price of one kilo of the blue star sugar.



Then the answer to the problem's question is: 

     the price of one kilogram mass of the red star sugar is 125% - 100% = 25% more 
     than the price of one kilogram mass of the blue star sugar.
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Solved.