Please explain how to get the answer to this. A mixture contains 30 grams of sugar and 50 grams of flour. How much flour must be added to make a mixture that is 75% flour?

Question

anonymous · Answer

You need to add 40 grams of flour to make it 90 grams of flour and 30 grams of sugar. You work this out because you know that 30 grams is going to be 25% so you times that by 3 to find 75% and you minus 50 grams from that to get 40 additional grams of flour

anonymous · Answer

what do you mean by 30 grams is going to be 25%? i got lost starting there.

anonymous · Answer

because you know that the sugar is going to be 25%, therefore 25% is going to be 30 grams

anonymous · Answer

oohh! you meant sugar. i get you now. thanks!!

anonymous · Answer

Let x grams of flour be added to make a mixture which then
has 75% flour. 
Then the mixture will weigh  ( 30 +50 +x ) grams = ( x +80 ) gms
Weight of flour in this mix : ( 50 + x ) gms
Hence the percentage of flour in the mix must then be 75%
     
ie  [ (50+x)/(x+80)] x 100 = 75

ie   100 x (x+50) = 75 X (x+80)

ie   4 ( x +50) = 3 (x+80)      [dividing both sides by 25]

ie   4x + 200 = 3x + 240

ie   4x - 3x = 240 - 200

ie   x = 40 gms

Thus 40 gms of flour must be added to the mix to increase
the percentage of flour to 75%.

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Verification:  When 40 gms fo flour is added the weight
of flour in the mix = 50 + 40 = 90gms

Weight of the mixture then = 30 + 50 + 40 = 120 gms

Hence the % of flour then = (90/120) x 100 % = (3/4)X100%

                                                                    = 75%
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