four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend…

Explanation:

Step1: Set up the equation

Let the amount of the 55% - spinach blend be $x$ cups. The amount of spinach in the 40% - spinach blend is $0.4\times4$ cups, and the amount of spinach in the 55% - spinach blend is $0.55x$ cups. The total amount of the resulting blend is $(4 + x)$ cups, and it contains 50% spinach, so the amount of spinach in the resulting blend is $0.5(4 + x)$ cups. Then we have the equation $0.4\times4+0.55x=0.5(4 + x)$.

Step2: Expand and simplify the equation

First, expand the right - hand side: $0.4\times4+0.55x = 0.5\times4+0.5x$. Calculate $0.4\times4 = 1.6$ and $0.5\times4 = 2$. So the equation becomes $1.6+0.55x=2 + 0.5x$.

Step3: Solve for $x$

Subtract $0.5x$ from both sides: $1.6+0.55x-0.5x=2 + 0.5x-0.5x$, which simplifies to $1.6 + 0.05x=2$. Then subtract 1.6 from both sides: $0.05x=2 - 1.6$, so $0.05x=0.4$. Divide both sides by 0.05: $x=\frac{0.4}{0.05}=8$.

Step4: Find the total amount of the resulting mixture

The total amount of the resulting mixture is $4 + x$ cups. Since $x = 8$, the total amount is $4+8=12$ cups.

Answer:

12