Question

Joe has 3 1/4 gallons of punch. He adds 1 1/2 quarts of juice to the punch. He drinks quart of punch. Which expression can be used to find the number of quarts of punch Joe has left? (1 gallon = 4 quarts)

Answer 1

The Solution:

Given that Joe has

`3(1)/(4)\text{gallons of punch}`

He added

`\begin{gathered} 1(1)/(2)\text{quarts of juice to the punch} \\ \text{Converting this to gallon, (since 1 gallon =4 quarts), we get} \\ 1(1)/(2)\text{quarts}=(3)/(2)*(1)/(4)=(3)/(8)\text{gallon} \end{gathered}`

He drinks

`(1)/(4)\text{quart}=(1)/(4)*(1)/(4)=(1)/(16)\text{gallon}`

Now, the expression that gives what is left with Joe is

`\begin{gathered} \text{ Let x represent Punch and y represent juice.} \\ So,\text{ we have} \\ 3(1)/(4)x+(3)/(8)y-(1)/(16)x \end{gathered}`

Simplifying, we get

`\begin{gathered} (13)/(4)x-(1)/(16)x+(3)/(8)y \\ \\ (52x-x)/(16)+(3)/(8)y \\ \\ (51x)/(16)+(3)/(8)y \end{gathered}`

Therefore, the required expression is

`(51)/(16)x+(3)/(8)y`