this is a proportional question.
32 oz. of juice are required to make 2 gallons of punch. 6 gallons of punch require n oz. of juice.
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