Applications invalving mixture

A jar of face cream contains 18% moisturizer, and another contains 24% moisturizer. How many ounces of each should be combined to get 12oz of a cream that is 22% moisturizer

Let the number of ounces of the 18% moisturizer  = x     so.......the number of 24% moisturizer  =  12 - x

And

(The number of oz of 18% product)* its concentration + (The number of oz of 24% product)* its concentration  = 

(The total number of ozs of product) * its concentration......mathematically, we have

(x)(.18)   + (12 - x) (.24)   =   (12)(.22)    remove the decimals by multiplying each side by 100

18x   + 24(12 -x)  = 22 * 12

18x  + 288 - 24x  = 264    

-6x + 288  = 264    subtract 288 from both sides

-6x  = -24     divide both sides by -6

x = 4 oz       this is the amount of 18% moisturizer that should be used

And  12 - x   = 12 - 4  = 8 oz   = the amount of 24% moisturizer that should be used

24f + 18(1 - f) = 22 where f is fraction of the 24% moisturiser

6f + 18 = 22

f = 2/3

2/3 of 12 is 8 so you need 8oz of the 24% stuff and 4oz of the 18% stuff to make 12oz of 22% moisturiser.