https://file.aiquickdraw.com/mathbot/file/17290418201934z6z5vbc.jpg

Let's break down the problem to find out how much flour Angela and Jaleel need if they each use all of their sugar.

### Angela's Recipe:
Looking at the graph for Angela's recipe, we can see the relationship between the amount of sugar and flour:
- For **1 cup** of sugar, she uses **1 cup** of flour.
- For **2 cups** of sugar, she uses **1.5 cups** of flour.
- For **3 cups** of sugar, she uses **2 cups** of flour.
- For **4 cups** of sugar, she uses **2.5 cups** of flour.
- For **5 cups** of sugar, she uses **3 cups** of flour.

### Jaleel's Recipe:
The table provides the relationship for Jaleel's recipe:
- For **1.5 cups** of sugar, he uses **1 cup** of flour.
- For **3 cups** of sugar, he uses **2 cups** of flour.
- For **4.5 cups** of sugar, he uses **3 cups** of flour.

### Shared Sugar:
They share a total of **20 cups** of sugar equally, which means each person gets:
\[
\frac{20}{2} = 10 \, \text{cups of sugar each}.
\]

### Flour for Angela:
From Angela's graph, we can see that the relationship between sugar and flour is **linear**. To calculate the exact amount of flour for 10 cups of sugar, we can use the slope of the line based on known values from the graph.

Between 1 and 5 cups of sugar:
- The slope = \(\frac{\Delta \text{flour}}{\Delta \text{sugar}} = \frac{3 - 1}{5 - 1} = \frac{2}{4} = 0.5\).

Therefore, the equation of the line is:
\[
\text{Flour} = 0.5 \times \text{Sugar}.
\]
For 10 cups of sugar, Angela needs:
\[
\text{Flour} = 0.5 \times 10 = 5 \, \text{cups of flour}.
\]

### Flour for Jaleel:
From Jaleel's table, we can also see that the relationship is linear. The slope can be calculated as:
\[
\frac{3 - 1}{4.5 - 1.5} = \frac{2}{3}.
\]
Thus, the equation for Jaleel's flour is:
\[
\text{Flour} = \frac{2}{3} \times \text{Sugar}.
\]
For 10 cups of sugar, Jaleel needs:
\[
\text{Flour} = \frac{2}{3} \times 10 = \frac{20}{3} = 6.67 \, \text{cups of flour}.
\]

### Final Answer:
- Angela needs **5 cups of flour**.
- Jaleel needs **6.67 cups of flour**.

Would you like more details or have any questions? 

Here are some related questions to think about:
1. How would the answer change if the sugar amount was different?
2. What if the slope for Angela's graph was steeper?
3. How could we calculate the sugar-to-flour ratio in another recipe?
4. What if Jaleel's table had more data points—how could we verify the linearity?
5. Could the relationship between sugar and flour ever be non-linear?

**Tip:** When working with graphs and tables, finding the slope and using linear equations can help extrapolate values for larger amounts.

Jaleel and Angela buy a 20-cup bag of sugar and divide it evenly to make their recipes. If they each use ALL of their sugar, how much flour do they each need?

This problem explores how to determine the amount of flour needed for Jaleel's and Angela's brownie recipes, based on a 20-cup bag of sugar they split evenly. Students will use the slope formula and linear equations to find the solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation