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

1 answer

Let's denote the unknown amount of salad blend containing 55% spinach as \( x \) cups. The mixture will then have a total volume of \( 4 + x \) cups.

First, we'll calculate the amount of spinach in each blend:

  1. For the salad blend containing 40% spinach: \[ \text{Amount of spinach from } 4 \text{ cups} = 0.40 \times 4 = 1.6 \text{ cups of spinach} \]

  2. For the salad blend containing 55% spinach: \[ \text{Amount of spinach from } x \text{ cups} = 0.55x \text{ cups of spinach} \]

Next, we combine these two amounts to find the total amount of spinach in the mixture: \[ \text{Total amount of spinach} = 1.6 + 0.55x \]

According to the problem, the resulting mixture must contain 50% spinach. Therefore, we can formulate the equation based on the total amount of spinach and the total volume of the mixture: \[ \frac{1.6 + 0.55x}{4 + x} = 0.50 \]

Now, we cross-multiply to solve for \( x \): \[ 1.6 + 0.55x = 0.50(4 + x) \] \[ 1.6 + 0.55x = 2 + 0.50x \]

Rearranging the equation: \[ 1.6 + 0.55x - 0.50x = 2 \] \[ 1.6 + 0.05x = 2 \]

Subtract \( 1.6 \) from both sides: \[ 0.05x = 2 - 1.6 \] \[ 0.05x = 0.4 \]

Dividing by \( 0.05 \): \[ x = \frac{0.4}{0.05} = 8 \]

Thus, the unknown amount of the salad blend is \( 8 \) cups. Now, we can find the total amount of salad in the resulting mixture: \[ 4 + x = 4 + 8 = 12 \text{ cups} \]

Therefore, the total amount of salad in the resulting mixture is \( \boxed{12} \) cups.