Q1: Predicting Chocolate Ice Cream Preference

You are given that the ratio of students who prefer chocolate ice cream to vanilla is $\frac{2}{3}$. To predict how many students in the entire grade of 240 prefer chocolate, you use the ratio to set up a proportion: $\frac{2}{3} = \frac{x}{240}$ where $x$ is the number of students who prefer chocolate ice cream.

Solving for $x$: $x = \frac{2}{3} \times 240 = 160$ So, 160 students are expected to prefer chocolate ice cream.

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Q2: Liam's Points in Basketball

The ratio of points scored by Elijah to Liam is $3:4$. If Elijah scored 12 points, you can set up the proportion to find Liam’s score: $\frac{3}{4} = \frac{12}{x}$ where $x$ is Liam's score.

Solving for $x$: $x = \frac{4}{3} \times 12 = 16$ So, Liam scored 16 points.

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Q3: Students Riding the Bus at Swanton Middle School

The ratio of students in Mia’s class who ride the bus is $\frac{5}{8}$. To estimate the number of students out of the 800 total who ride the bus, set up a proportion: $\frac{5}{8} = \frac{x}{800}$ where $x$ is the total number of students who ride the bus.

Solving for $x$: $x = \frac{5}{8} \times 800 = 500$ So, 500 students are expected to ride the bus.

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Q4: People Who Prefer Eggs

The ratio of people who prefer oatmeal to those who prefer eggs is $3:5$. If 21 people said they prefer oatmeal, set up the proportion: $\frac{3}{5} = \frac{21}{x}$ where $x$ represents the number of people who prefer eggs.

Solving for $x$: $x = \frac{5}{3} \times 21 = 35$ So, 35 people prefer eggs.

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Do you want more details or have any questions?

Here are 5 related questions:

1. How can you express a ratio as a fraction in simplest form?
2. What is the difference between a ratio and a proportion?
3. If 75 out of 100 people prefer chocolate, what ratio describes this preference?
4. How can you determine the total number of outcomes if given a ratio?
5. What are some real-world scenarios where ratios and proportions are used?

Tip: To solve proportions, cross-multiply and then divide to isolate the unknown variable.