How to Solve Crazy Mixture Problems

Hi,

Don’t be misled by the title of the post. I used to think the same about the mixture problems. It’s not that I found them way too difficult to solve. It’s just that the approach or method that I used to solve them was lengthy and complicated.

Let’s take an example:

Example: A farmer has 100 gallons of juice mixture which has 70% juice. He wishes to mix it with another mixture which as 90% juice, to obtain a 75% juice. How much of 90% juice must he mix??

Old Approach:

I used to draw a 2 x 2 matrix and draw columns before, after, desired and so on …..

New Approach:

Applying this formula now –

Let x be the volume of 90% solution.

100 (0.7) + x (0.9) = 0.75(x+100)

70 + 0.9x = 0.75x + 75

0.15x = 5

x = 33 1/3 gallons.

Second type of questions asks in what ratio should the two mixture be mixed to get a new mixture.

This question requires little to no calculation.

Let’s modify the above question and see an example.

Example: A farmer contains a juice mixture which has 70% juice. He wishes to mix it with another mixture which as 90% juice, in order to obtain 75% of 100 litres juice.

a) In what ratio should the mixture be mixed??

b) How many litres of mixture 1 and how many litres of mixture 2 is required??

Explanation: I am sure everyone as a child have sat on a see-saw. A mixture problem like this is just like a saw. If a heavier boy sits on one end of the see saw, then the lighter boy must move as far as possible to balance the wight. The same concept is used here to solve the problem.

70%(Sol A)————————75%(Final Sol) ——————————-90%(Sol B)

Now how far is 70 from 75 ====> 5

How far is 75 from 90 ========> 15

So to find the ratios, we just reverse the difference

SolA/SolB = 15/5. =====> 3/1 ratio. This solves the first part.

Second partis simpler now. How much of Sol A is required

Sol A = 3/4 * 100 = 75

Sol B = 1/4 * 100 = 25

Almost all the problems can be solved using this approach. I just never could get around the formula or concept earlier and was using the general approach of MGMAT maths, which was taking a lot of time for me and was confusing me. This session was covered in knewton session and it just blew me off, because the approach was so simple.

Here a screenshot of the page that I found on some url today.

~ ciao