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.

Question

How many cups of salad are in the resulting mixture?

8
9
12
13

Answer 1

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 $\boxed{{\displaystyle 12}}$ cups.