The problem given involves understanding the ratio of cups of water to cups of flour that Leo needs for making plaster.

Problem Breakdown

The initial information states:

• Leo mixes 2 cups of flour with 7 cups of water.

Let's examine each question.

Part (a)

Question: How many cups of water does Leo use for every 1 cup of flour that he uses?

Since the ratio of flour to water is given as 2 cups of flour to 7 cups of water, we can set up the ratio: $\frac{7 \text{ cups of water}}{2 \text{ cups of flour}} = \frac{7}{2} \text{ cups of water per cup of flour}$

This simplifies to 3.5 cups of water for every 1 cup of flour.

Part (b)

Question: How many cups of flour does Leo use for every 1 cup of water that he uses?

Here, we take the reciprocal of the original ratio, which was 2 cups of flour for 7 cups of water: $\frac{2 \text{ cups of flour}}{7 \text{ cups of water}} = \frac{2}{7} \text{ cups of flour per cup of water}$

So, Leo uses 2/7 cups of flour for every 1 cup of water.

Part (c)

Question: If Leo uses 9 cups of flour, how many cups of water should he use?

Since we know that the ratio of flour to water is 2:7, we can set up a proportion: $\frac{2 \text{ cups of flour}}{7 \text{ cups of water}} = \frac{9 \text{ cups of flour}}{x \text{ cups of water}}$

Solving for $x$: $x = \frac{9 \times 7}{2} = 31.5 \text{ cups of water}$

So, if Leo uses 9 cups of flour, he should use 31.5 cups of water.

Would you like further details on the calculations or have any other questions?

Related Questions

1. If Leo uses 5 cups of flour, how much water should he use?
2. What is the ratio of water to total mixture (flour + water) in simplest form?
3. If Leo wanted to make half the quantity, how much flour and water would he need?
4. How many cups of plaster will Leo have in total if he uses the original ratio?
5. If Leo doubles the water but keeps the flour the same, what will the new ratio of flour to water be?

Tip

When dealing with ratios, it can be helpful to keep them in fraction form to simplify comparisons and proportional calculations.