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32 oz. of juice are required to make 2 gallons of punch. 6 gallons of punch require n oz. of juice.

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3 Answers

You are given that 32 ounces of juice make 2 gallons of punch. With this, you are asked to find how many ounces of juice (n) are needed to make 6 gallons of juice. This is, in fact, a proportionality problem and one way of approaching is by the following:

         32 ounces / 2 gallons  =  n ounces / 6 gallons

                             32 / 2  =  n / 6

          cross multiply and solve for n 

                               32 · 6  =  2 · n

                                   192 = 2n      

          divide both sides of the equation by 2 

                                     96 = n

     Therefore, 96 ounces of juice are required to make 6 gallons of punch. 

Set it up as a ratio of Juice to punch (juice/punch):

(32 oz juice)/(2 gal punch) = (n oz juice)/(6 gal punch)

Multiply each side by 6 to isolate n:

(6 gal punch)(32 oz juice)/(2 gal punch) = n

(3)(32 oz juice) = n

n = 96 oz juice

In setting a proportional question, remember that you are trying to create two fractions, where the numerators have one type of units and the denominators have another.

For this problem, I am going to make the oz. of juice the numerators and the gallons of punch the denominator.

32/2 = n/6                      32 oz to 2 G = n oz to 6 G

16 = n/6                         Simplify the fraction

6(16) = 6(n/6)                Multiply each side by 6

96 = n                           Simplify

You need 96 oz. of juice