https://file.aiquickdraw.com/mathbot/file/1727711796159jam1ut77.jpg

Let's break down the two problems on the worksheet and work through the solutions:

### 1. Feeding a Crowd (Rice Problem)

- **Given Information:**
  - 2 cups of dry rice serve 6 people.

- **Part a: How many people will 10 cups of rice serve?**

We know from the table that 2 cups of rice serve 6 people. To find how many people 10 cups will serve, we can set up a proportion based on this relationship:

\[
\frac{2 \text{ cups}}{6 \text{ people}} = \frac{10 \text{ cups}}{x \text{ people}}
\]

Cross-multiply:

\[
2x = 10 \times 6
\]
\[
2x = 60
\]
\[
x = \frac{60}{2} = 30
\]

Thus, **10 cups of rice will serve 30 people**.

- **Part b: How many cups of rice are needed to serve 45 people?**

We use the same ratio (2 cups for 6 people) and set up a proportion to solve for the number of cups needed:

\[
\frac{2 \text{ cups}}{6 \text{ people}} = \frac{y \text{ cups}}{45 \text{ people}}
\]

Cross-multiply:

\[
6y = 2 \times 45
\]
\[
6y = 90
\]
\[
y = \frac{90}{6} = 15
\]

Thus, **15 cups of rice are needed to serve 45 people**.

### 2. Spring Rolls Problem

- **Given Information:**
  - 6 spring rolls serve 3 people.

We can again use proportions to complete the table.

- **For 30 spring rolls:**
\[
\frac{6 \text{ spring rolls}}{3 \text{ people}} = \frac{30 \text{ spring rolls}}{x \text{ people}}
\]

Cross-multiply:

\[
6x = 30 \times 3
\]
\[
6x = 90
\]
\[
x = \frac{90}{6} = 15
\]

Thus, **30 spring rolls will serve 15 people**.

- **For 40 spring rolls:**
\[
\frac{6 \text{ spring rolls}}{3 \text{ people}} = \frac{40 \text{ spring rolls}}{x \text{ people}}
\]

Cross-multiply:

\[
6x = 40 \times 3
\]
\[
6x = 120
\]
\[
x = \frac{120}{6} = 20
\]

Thus, **40 spring rolls will serve 20 people**.

---

If you have any questions or want further explanation, feel free to ask! Here are five questions related to this topic:

1. How would the proportions change if 3 cups of rice served 9 people?
2. What if you had to serve 100 people? How many cups of rice would be needed?
3. How can you use unit rates to solve these problems instead of proportions?
4. Can this method be applied to other recipes, and how?
5. What if the ratio of rice to people changes with different quantities?

**Tip:** When solving proportions, always make sure the units match across the ratio before cross-multiplying.

How many people will 10 cups of rice serve? How many cups of rice are needed to serve 45 people? And how many people can be served with 30 and 40 spring rolls?

This lesson covers solving proportion problems involving rice and spring rolls. Learn how to determine the number of people served by a given amount of food using ratios and cross-multiplication. Suitable for Grade 7 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation