Lesson INTRODUCTION - Mixture Questions

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 This Lesson (INTRODUCTION - Mixture Questions) was created by by longjonsilver(2297)  : View Source, ShowAbout longjonsilver: I have a new job in September, teaching Introduction These types of "English into Algebrese" questions seem to cause students a lot of problems. In essence, the approach to use is: INITIAL STATE + ADDITION = FINAL STATE SO, lets look at an example. EXAMPLE Q: A vat contains 90kg of powdered milk and 10kg of sugar. How much more sugar must be added to the mixture to make a 25% sugar mix? A: Consider the sugar, as that is what the question is about. Initially: the total amount in the mixture is (10+90) --> 100kg. We therefore get that (10/100) is the fraction of sugar, initially. Now add some sugar, Let this be x. This will increase the amount of sugar and also the total amount of the mixture, giving: Finally: (10+x)/(100+x) is the new fraction of sugar. We are told that the final fraction of sugar is 0.25 (--> the 25%: ie 25 out of 100) So, we have --> x = 20kg and now CHECK that it makes sense: final mix is , which becomes --> 1/4 --> 25% so therefore correct. EXAMPLE Q: How many kilogram of fine glucose must be added to 25 kilograms of a 12% sweetened juice concentrate to prepare instead a light syrup 20% sweet? A: Consider the glucose, as that is what the question is about. Initially: there is 12% glucose in the mixture. This is 12% of 25kg. In other words, (12/100)*25 --> 3kg of glucose. So, we have 3/25 as the initial fraction of glucose --> the 12%. We then add some more. Let this be xkg. Finally: we end up with as the fraction of glucose. We are told that this needs to be 20% ie 0.20. So we have --> x = 2/0.80 --> x = 2.5kg Now, do the CHECK we had , which becomes --> 0.20 which is 20%. This lesson has been accessed 8351 times.