Question
Abdul loves to make fresh lemonade in the summer. In his recipe, he uses 2 cups of sugar for every 3 cups of lemon juice.
Complete the table.
Cups of lemon juice 3 9
Cups of sugar 2 10 12
Graph the data from the table.
Complete the table.
Cups of lemon juice 3 9
Cups of sugar 2 10 12
Graph the data from the table.
Answers
GPT-4o mini
To complete the table based on Abdul's recipe of using 2 cups of sugar for every 3 cups of lemon juice, we can set up a proportion:
Given:
- For every 3 cups of lemon juice, he uses 2 cups of sugar.
Let's fill in the missing values in the table.
### Initial Data:
1. Cups of lemon juice: 3
- Sugar: 2 cups (already provided).
2. Cups of lemon juice: 9
- Using the proportion (2 cups sugar / 3 cups lemon juice):
- \( \text{Sugar} = \left( \frac{2 \text{ cups of sugar}}{3 \text{ cups of lemon juice}} \right) \times 9 \)
- \( = \frac{2 \times 9}{3} = 6 \)
- Therefore, for 9 cups of lemon juice, we need 6 cups of sugar.
3. Cups of lemon juice: (missing value)
- Looking at the previous row (Cups of sugar: 10), we can find the amount of lemon juice needed:
- Using the proportion:
- \( \text{Lemon Juice} = \left( \frac{3 \text{ cups of lemon juice}}{2 \text{ cups of sugar}} \right) \times 10 \)
- \( = \frac{3 \times 10}{2} = 15 \)
- Therefore, for 10 cups of sugar, we need 15 cups of lemon juice.
4. Cups of sugar: 12
- Using the proportion:
- \( \text{Lemon Juice} = \left( \frac{3 \text{ cups of lemon juice}}{2 \text{ cups of sugar}} \right) \times 12 \)
- \( = \frac{3 \times 12}{2} = 18 \)
- Therefore, for 12 cups of sugar, we need 18 cups of lemon juice.
### Completed Table:
| Cups of lemon juice | 3 | 9 | 15 | 18 |
|---------------------|---|---|----|----|
| Cups of sugar | 2 | 6 | 10 | 12 |
### Graphing the Data:
To graph this data, plot the points on a coordinate system where the x-axis represents cups of lemon juice and the y-axis represents cups of sugar.
**Points for the graph:**
1. (3, 2)
2. (9, 6)
3. (15, 10)
4. (18, 12)
The graph would display a linear relationship showing that as the number of cups of lemon juice increases, the number of cups of sugar also increases proportionally. The line can be drawn through these points, demonstrating the relationship:
\[ \text{Sugar} = \frac{2}{3} \times \text{Lemon Juice} \]
This can be represented in equation form, and both axes should be labeled accordingly.
Given:
- For every 3 cups of lemon juice, he uses 2 cups of sugar.
Let's fill in the missing values in the table.
### Initial Data:
1. Cups of lemon juice: 3
- Sugar: 2 cups (already provided).
2. Cups of lemon juice: 9
- Using the proportion (2 cups sugar / 3 cups lemon juice):
- \( \text{Sugar} = \left( \frac{2 \text{ cups of sugar}}{3 \text{ cups of lemon juice}} \right) \times 9 \)
- \( = \frac{2 \times 9}{3} = 6 \)
- Therefore, for 9 cups of lemon juice, we need 6 cups of sugar.
3. Cups of lemon juice: (missing value)
- Looking at the previous row (Cups of sugar: 10), we can find the amount of lemon juice needed:
- Using the proportion:
- \( \text{Lemon Juice} = \left( \frac{3 \text{ cups of lemon juice}}{2 \text{ cups of sugar}} \right) \times 10 \)
- \( = \frac{3 \times 10}{2} = 15 \)
- Therefore, for 10 cups of sugar, we need 15 cups of lemon juice.
4. Cups of sugar: 12
- Using the proportion:
- \( \text{Lemon Juice} = \left( \frac{3 \text{ cups of lemon juice}}{2 \text{ cups of sugar}} \right) \times 12 \)
- \( = \frac{3 \times 12}{2} = 18 \)
- Therefore, for 12 cups of sugar, we need 18 cups of lemon juice.
### Completed Table:
| Cups of lemon juice | 3 | 9 | 15 | 18 |
|---------------------|---|---|----|----|
| Cups of sugar | 2 | 6 | 10 | 12 |
### Graphing the Data:
To graph this data, plot the points on a coordinate system where the x-axis represents cups of lemon juice and the y-axis represents cups of sugar.
**Points for the graph:**
1. (3, 2)
2. (9, 6)
3. (15, 10)
4. (18, 12)
The graph would display a linear relationship showing that as the number of cups of lemon juice increases, the number of cups of sugar also increases proportionally. The line can be drawn through these points, demonstrating the relationship:
\[ \text{Sugar} = \frac{2}{3} \times \text{Lemon Juice} \]
This can be represented in equation form, and both axes should be labeled accordingly.