Seven up

Peter Barman is making 8 gallons of Tropical Trip Punch. He has already poured in 1 3/4 gal pineapple juice and 2 1/2 gal orange juice. The only other ingredient is 7-Up. How much does 7-Up Peter need?

Correct answer:

x =  3 ³⁄₄ = 15/4 gal

Step-by-step explanation:

$$\begin{gathered} V=8\text{gal} \\ {V}_1=1\frac{3}{4}=1+\frac{3}{4}=\frac{1\cdot 4+3}{4}=\frac{4+3}{4}=\frac{7}{4}=1.75\text{gal} \\ {V}_2=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2.5\text{gal} \\ x=V-V_1-V_2=8-\frac{7}{4}-\frac{5}{2}=\frac{15}{4}\text{gal}=3\frac{3}{4}\text{gal}=3.75\text{gal} \end{gathered}$$

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