Question

You are getting ready for your graduation party, so you buy 10 cases of soda. Each case has 24 cans of soda and each can holds 12 fluid ounces. How many gallons of soda did you purchase?Hint: 1 cup = 8 fluid ounces

Answer 1

We have 10 cases of soda. If each case has 24 cans and each can holds 12 fluid ounces, we calculate how many fluid ounces of soda we purchased:

`x=10*24*12=2880\text{ fluid ounces}`

But we need to know how many gallons of soda we purchased. Using the following conversion rules:

`\begin{gathered} 1\text{ cup }=8\text{ fluid ounces} \\ 1\text{ gallon }=16\text{ cups} \end{gathered}`

Then, we multiply the first one by 360 on both sides to obtain 2880 fluid ounces:

`\begin{gathered} 360*1\text{ cup }=360*8\text{ fluid ounces} \\ \\ \Rightarrow360\text{ cups}=2880\text{ fluid ounces} \end{gathered}`

Finally, we multiply the second conversion rule by 22.5 to obtain 360 cups:

`\begin{gathered} 22.5*1\text{ gallon }=22.5*16\text{ cups} \\ \\ \therefore22.5\text{ gallons }=360\text{ cups} \end{gathered}`

Answer: 22.5 gallons