Question

1. matt heard the best way to clean hardwood floors is with water and vinegar. the recipe calls for 2 cups of water per $\frac{1}{2}$ cup of vinegar. he uses 20 cups of water to fill the bucket to clean all of the hardwood floors. how much vinegar does he need to add?

5 cups

10 cups

2 cups

20 cups

Explanation:

Step1: Find the ratio of water to vinegar

The recipe has 2 cups of water per $\frac{1}{2}$ cup of vinegar. So the ratio of water to vinegar is $2:\frac{1}{2}$. Simplifying this ratio, we can write it as a fraction: $\frac{\text{water}}{\text{vinegar}}=\frac{2}{\frac{1}{2}} = 4$. This means for every 4 cups of water, we need 1 cup of vinegar? Wait, no, let's re - calculate. If 2 cups of water correspond to $\frac{1}{2}$ cup of vinegar, then the amount of vinegar per cup of water is $\frac{\frac{1}{2}}{2}=\frac{1}{4}$ cup of vinegar per cup of water.

Step2: Calculate the amount of vinegar for 20 cups of water

We know that for each cup of water, we need $\frac{1}{4}$ cup of vinegar. If we have 20 cups of water, then the amount of vinegar $V$ is given by $V = 20\times\frac{1}{4}$. Wait, another way: Let $x$ be the amount of vinegar. We can set up a proportion. $\frac{2}{\frac{1}{2}}=\frac{20}{x}$. Cross - multiplying, we get $2x=20\times\frac{1}{2}$. Then $2x = 10$, and $x = 5$.

Answer:

5 cups (The correct option is the one with "5 cups")