Seven up

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

Correct answer:

x =  3.75 gal

Step-by-step explanation:

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

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