Question

$8$June needs $48$gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?

Short answer

The bigger cooler can hold $40$gallons and the smaller one can hold $8$ gallons

Step-by-step solution

Step 1. Given

June needs $48$gallons of punch.

He has a bigger and smaller cooler.

Step 2. From equation

Let $x$represent the bigger cooler and $y$represent the smaller cooler.

June has a total of $48$gallons and he has bigger and smaller coolers.

So, $x+y=48$

The bigger cooler is five times that of smaller cooler.

So, $x=5y$

Step 3. Solve the equations

Substitute $x=5y$in the first equation,

$5y+y=48$

$6y=48$

Divide both sides by, $6$,

$y=8$

The smaller cooler can hold $8$ gallons

Step 4. Solve for x

Substitute $y=8$in the equation,

$x=5y$

$x=5\left(8\right)$

$x=40$

The bigger cooler can hold $40$ gallons

Step 5. Check the answers

Substitute $x=40,$

localid="1658855700530" $y=8$in the first equation,

$x+y=48$

$\left(40\right)+\left(8\right)=48$

Hence the equation holds true.