Q 85 - Intermediate Algebra

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?

Step-by-Step Solution

Answer

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

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 $x=40,$

                  $y=8$ in the first equation,

             $x+y=48$

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

Hence the equation holds true.