Question

four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containing 55% spinach. the resulting salad contains 50% spinach. how many cups of salad are in the resulting mixture? 8 9 12 13

Explanation:

Step1: Define the variable

Let \( x \) be the number of cups of the 55% spinach salad blend. The total number of cups in the resulting mixture will be \( 4 + x \).

Step2: Set up the equation based on spinach content

The amount of spinach in the 40% blend is \( 0.40 \times 4 \), the amount of spinach in the 55% blend is \( 0.55x \), and the amount of spinach in the resulting 50% blend is \( 0.50(4 + x) \). So we have the equation:

$$ 0.40 \times 4 + 0.55x = 0.50(4 + x) $$

Step3: Solve the equation

First, calculate \( 0.40 \times 4 = 1.6 \). The equation becomes:

$$ 1.6 + 0.55x = 2 + 0.50x $$

Subtract \( 0.50x \) from both sides:

$$ 1.6 + 0.05x = 2 $$

Subtract 1.6 from both sides:

$$ 0.05x = 0.4 $$

Divide both sides by 0.05:

$$ x = \frac{0.4}{0.05} = 8 $$

Step4: Find the total number of cups

The total number of cups in the resulting mixture is \( 4 + x = 4 + 8 = 12 \).

Answer:

12