Question

4) There are 5 gallons of lemonade in a container. Sylvia fills glasses with 1/8 of a gallon of lemonade from the container. How many gallons of lemonade are left in the container if Sylvia fills: a) 7 glasses? LILAH b) 20 glasses? TRE c) 32 glasses?

Answer 1

Part a). If Sylvia fills 7 glasses, then the amount of lemonade she serves is 7/8 of a gallon

`7\cdot(1)/(8)=(7)/(8)`

Therefore, the amount of lemonade left in the container will be 33/8 gallons.

`5-(7)/(8)=(5)/(1)-(7)/(8)=(5\cdot8)/(1\cdot8)-(7)/(8)=(40)/(8)-(7)/(8)=(40-7)/(8)=(33)/(8)`

Part b). If Sylvia fills 20 glasses, then the amount of lemonade she serves is 5/2 gallons

`\begin{gathered} 20\cdot(1)/(8)=(20)/(8) \\ \text{Simplifying} \\ (20)/(8)=(5\cdot4)/(2\cdot4)=(5)/(2) \end{gathered}`

Therefore, the amount of lemonade left in the container will be 5/2 gallons

`5-(5)/(2)=(5)/(1)-(5)/(2)=(5\cdot2)/(1\cdot2)-(5)/(2)=(10)/(2)-(5)/(2)=(10-5)/(2)=(5)/(2)`

Part c). If Sylvia fills 32 glasses, then the amount of lemonade she serves is 4 gallons

`32\cdot(1)/(8)=(32)/(8)=4`

Now, the amount of lemonade left in the container will be 1 gallon

`5-4=1`