Achemical company makes two brands of antifreeze. the first brand is 35% anti freeze, and the second brand is 85% pure antifreeze. in order to obtain 150 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used.

There are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.

Step-by-step explanation:

Since we have given that

Percentage of anti freeze in first brand = 35%

Percentage of anti freeze in second brand = 85%

Percentage of anti freeze in mixture = 75%

Total number of gallons of mixture = 150 gallons

We will use " Mixture and Allegation":

 First brand         Second brand

      35%                      85%

                      75%

------------------------------------------------------------------

85%-75%         :            75%-35%

    10                :               40

     1                 :                 4

So, Number of gallons of anti freeze in first brand is given by

Number of gallons of anti freeze in second brand is given by

Hence, there are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.

tangent

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,