Q 94 - Intermediate Algebra

Question

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make $64$ ounces of strawberry infused water?

Step-by-Step Solution

Answer

Molly needs $16$ ounces of strawberry juice and $48$ ounces of water to make $64$ ounces of strawberry infused water.

Step 1. Given

For each ounce of strawberry juice, she uses three times as many ounces of water as juice. 

She is making $64$ ounces of strawberry infused water.

Step 2. Form linear equation

Let $x$ represent the number of ounce of strawberry juice.

And $y$ represent the number of ounce of water.

For strawberry infused water, Molly mixes strawberry juice with water

$x+y=64$

For each ounce of strawberry juice, she uses three

times as many ounces of water as juice. 

So, $y=3x$

Step 3. Solve linear equation

Solve the system of linear equations

$x+y=64$

     $y=3x$

Substitute $y=3x$ in the first equation,

$x+3x=64$

      $4x=64$

Divide both sides of the equation by $4$,

        $x=16$

The number of ounce of strawberry juice is $16$ ounces.

Step 4. Solve for y

Substitute $x=16$ in the second equation,

$y=3x$

$y=3\left(16\right)$

$y=48$

The number of ounces of water is $48$ ounces.

Step 5. Check the answer

Substitute $x=16$,

                  $y=48$ in the first equation,

    $x+y=64$

$16+48=64$

        $64=64$

Hence the equation holds true.