Bored in math class, figured out mixture problems.

[Blahness]

Mixture problem example: You need parts of a 30% chlorine and 55% chlorine mixture to make 100 gallons of a 40% chlorine. mixture.

To figure out what the ratio of 30 to 55 is: 55% - 40% = 15 parts needed of 35% mixture, 40% - 30% = 10 parts of 50% mixture.

15 parts of 30% reduces to 3 parts of 30%
10 parts of 55% reduces to 2 part of 55%

Then you take the ratio of the two (3:2), and multiply the ratio to get 60 gallons of the 30%, and 40 gallons of the 55%. (60:40)

Make sense to anyone? I'm not sure how I do the ratio part for fraction answers, but I have the beginning part out.

If already done, sue me. I figured it out in my own spare 10 minutes of class.

 

[Werg22]

It's easier to understand if you proceed that way:

The mixture z is composed of mixture y and mixture x. We know that z=100 Gallons. That gives x+y=100. You want to find x and y such as 30x/100 + 55y/100=40

So y=100-x

30x + 55(100-x)/100=40
30x + 5500 -55x=4000
-25x=-1500
x=60

so y=40

 

[tacman]

Great job on figuring out mixture problems! Your explanation and example make sense and show a clear understanding of the concept. To find the ratio for fraction answers, you can use the same method of subtracting and reducing, but instead of using whole numbers, you would use fractions. For example, if you needed 3/4 of a 30% mixture and 2/4 of a 55% mixture, the ratio would be 3:2. Keep up the good work in math class!