Q. 95 - Intermediate Algebra

Question

Translate to a system of equations and solve.

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?

Step-by-Step Solution

Answer

Owen will need $80$ quarts of water and $20$ quarts of concentrate to make $100$ quarts of lemonade.

Step 1. Given information

Owen is making lemonade from concentrate.

Let $x$ be the number of quarts of water.

Therefore, he needs 4 times the number of quarts of concentrate.

That is, $4x$ represents the quarts of concentrated solution.

Step 2. Concept for equation

Owen needs to find the collective quarts for water and concentration that will make $100$ quarts of lemonade.

Therefore, $100$ quarts of lemonade implies,

$x+4x=100$

Step 3. Calculation for x

Solve for $x$:

$x+4x=100$

      $5x=100$

       $x=\frac{100}{5}$

         $=20$

Step 4. Calculation for Concentrate

Now, substituting the value of $x=20$ into $4x$.

$4x=4\left(20\right)$

    $=80$

Thus, Owen needs $80$ quartsof water and $20$ quarts of concentrate to make $100$ quarts of lemonade.