For a school project, Layla makes a paste made from only two ingredients: flour and water. The ratio table shows the relationship between the number of cups of flour and the total number of cups of paste she can make. What is the ratio of flour to water in the paste?

Question

Paste Mixture
Cups of Flour
Cups of Paste
3
4
6
8
9
12
12
16
1:3
3:4
4:3
3:1

Answer 1

To determine the ratio of flour to water in the paste, we first need to analyze the information provided in the ratio table.

From the table, we have:

• When Layla uses 3 cups of flour, she makes 4 cups of paste.
• When Layla uses 6 cups of flour, she makes 8 cups of paste.
• When Layla uses 9 cups of flour, she makes 12 cups of paste.
• When Layla uses 12 cups of flour, she makes 16 cups of paste.

To find the amount of water in each case, we can use the formula:

\[ \text{Water} = \text{Total Paste} - \text{Flour} \]

Let's calculate the water in each scenario:

1. 3 cups of flour → 4 cups of paste:

   • Water = 4 - 3 = 1 cup of water

2. 6 cups of flour → 8 cups of paste:

   • Water = 8 - 6 = 2 cups of water

3. 9 cups of flour → 12 cups of paste:

   • Water = 12 - 9 = 3 cups of water

4. 12 cups of flour → 16 cups of paste:

   • Water = 16 - 12 = 4 cups of water

Now we can summarize the ratios of flour to water in each case:

1. For 3 cups of flour and 1 cup of water: Ratio = \(3:1\)
2. For 6 cups of flour and 2 cups of water: Ratio = \(6:2\) which simplifies to \(3:1\)
3. For 9 cups of flour and 3 cups of water: Ratio = \(9:3\) which simplifies to \(3:1\)
4. For 12 cups of flour and 4 cups of water: Ratio = \(12:4\) which simplifies to \(3:1\)

In all scenarios, the ratio of flour to water in Layla's paste is 3:1.