Lesson INTRODUCTION - Mixture Questions

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%.