SOLUTION: 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

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Question 1208072: 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?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~ 

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%2Fx.



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%2Fx  is

    y%2Fx = %28m%2A1.5%29%2F%281.2%2Am%29 = reduce m in the numerator and denominator = 1.5%2F%281.2%29 = 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.

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


"The mass of a bag of red star sugar is 20% greater than the mass of a bag of blue star sugar."

Arbitrarily, suppose the bag of red star sugar is 6kg and the bag of blue star sugar is 5kg.

"However, a bag of red star sugar costs 50% more than a bag of blue star sugar."

Arbitrarily, suppose the bag of red star sugar costs $3 and the bag of blue star sugar costs $2.

"For the same mass, red star sugar costs how much percent more than blue star sugar?"

The cost per kg of the red star sugar is $3/6kg = $0.50; the cost per kg of the blue star sugar is $2/5kg = $0.40.

The ratio of the costs per kg of the red and blue sugars is $0.50/$0.40 = 5/4 = 1.25 = 125%; so for the same mass the red star sugar costs 25% more then the blue star sugar.