Collin

Collin is making fruit for a birthday party using the recipe below
Ingredients

Pink lemonade	1 1/2 gal
Seltzer water	2 3/4 gal
Fruit juice	7/8 gal

Collin is using a punch bowl that holds 8 gallons of punch. How much more punch could Collin make the extra space in the bowl?

Final Answer:

x =  2 ⁷⁄₈ = 23/8 gal

Step-by-step explanation:

$$\begin{gathered} a=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1.5\text{gal} \\ b=2\frac{3}{4}=2+\frac{3}{4}=\frac{2\cdot 4+3}{4}=\frac{8+3}{4}=\frac{11}{4}=2.75\text{gal} \\ c=7/8=\frac{7}{8}=0.875\text{gal} \\ {V}_1=a+b+c=\frac{3}{2}+\frac{11}{4}+\frac{7}{8}=\frac{12}{8}+\frac{22}{8}+\frac{7}{8}=\frac{12+22+7}{8}=\frac{41}{8}=5.125\text{gal} \\ {V}_2=8\text{gal} \\ x=V_2-V_1=8-\frac{41}{8}=\frac{8\cdot 8}{8}-\frac{41}{8}=\frac{64}{8}-\frac{41}{8}=\frac{64-41}{8}=\frac{23}{8}=\frac{23}{8}\text{gal}=2\frac{7}{8}\text{gal}=2.875\text{gal} \end{gathered}$$

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