https://file.aiquickdraw.com/mathbot/file/1729041482596ks83t7uz.jpg

Let's break down the problem systematically.

### Given:
1. **20 cups of sugar** are divided evenly between Angela and Jaleel.
   - This means **each gets 10 cups of sugar**.

2. **Angela's Recipe**: Shown in the graph.
3. **Jaleel's Recipe**: Shown in the table:
   - 1.5 cups sugar → 1 cup flour  
   - 3 cups sugar → 2 cups flour  
   - 4.5 cups sugar → 3 cups flour  

4. **Goal**: We need to figure out **how much flour** each of them will use if they use **all of their sugar**.

---

### Step 1: Analyze the Data from Angela's Graph

From the **graph**, let's gather some points that show the sugar-to-flour relationship:
- (1, 1.5) means 1 cup of sugar needs 1.5 cups of flour.
- (2, 2) means 2 cups of sugar needs 2 cups of flour.
- (3, 2.5) means 3 cups of sugar needs 2.5 cups of flour.
- (4, 3) means 4 cups of sugar needs 3 cups of flour.
- (5, 3.5) means 5 cups of sugar needs 3.5 cups of flour.

It looks like the amount of **flour increases by 0.5 cups for every 1 additional cup of sugar**.

---

### Step 2: Calculate Flour for 10 Cups of Sugar

#### Angela's Recipe:
From the pattern in the graph, for every 1 cup of sugar, the flour increases by 0.5 cups.  
- For 10 cups of sugar, the amount of flour will be:
  \[
3.5 + (5 \times 0.5) = 6 \, \text{cups of flour}.
  \]

#### Jaleel's Recipe:
The table shows a **linear relationship** between sugar and flour. The pattern is:
- For every 1.5 cups of sugar, 1 more cup of flour is needed.

We need to figure out how much flour is needed for **10 cups of sugar**.  
The ratio from the table is \( \frac{2}{3} \) (since 3 cups of sugar needs 2 cups of flour).

Thus, for 10 cups of sugar:
\[
\frac{2}{3} \times 10 = \frac{20}{3} \approx 6.67 \, \text{cups of flour}.
\]

---

### Step 3: Summary of Answers
- **Angela**: 6 cups of flour.  
- **Jaleel**: 6.67 cups of flour (or \( \frac{20}{3} \) cups).

---

Would you like further details, such as how to interpret linear relationships more deeply? Here are some follow-up questions for practice:

1. How can you use a proportion to solve similar sugar-flour relationships?
2. What would the flour amount be if Angela used only 5 cups of sugar?
3. If Jaleel had only 7.5 cups of sugar, how much flour would he need?
4. How do you determine the slope of Angela’s sugar-flour graph?
5. What other scenarios could arise if they shared flour instead of sugar?

**Tip**: Always check whether a relationship is proportional (linear with a consistent ratio) when dealing with graphs and tables in problems like this.

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?

In this problem, Jaleel and Angela each use 10 cups of sugar from a shared 20-cup bag to make their brownie recipes. Learn how to calculate the required amount of flour for each based on proportional and linear relationships, using graphs and tables. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation