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Flashcards: Extrapolating Linear Proportions

You are planning a party. The maximum number of people the reception hall can hold is $\displaystyle 1$ person for every $\displaystyle 5$ square feet of space. If the hall is $\displaystyle 60$ feet wide and $\displaystyle 50$ feet long, how many people can you invite?

1500 $\displaystyle 1500$

2500 $\displaystyle 2500$

600 $\displaystyle 600$

500 $\displaystyle 500$

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Flashcards: Extrapolating Linear Proportions

1500 $\displaystyle 1500$

2500 $\displaystyle 2500$

600 $\displaystyle 600$

500 $\displaystyle 500$

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Flashcards: Extrapolating Linear Proportions

Your answer:

1500 $\displaystyle 1500$

Your answer:

2500 $\displaystyle 2500$

Your answer:

500 $\displaystyle 500$

Correct answer:

600 $\displaystyle 600$

Explanation:

Total area of hall $=60ft*50ft=3000ft^{2}$ $\displaystyle =60ft*50ft=3000ft^{2}$

At $\displaystyle 1$ person per $\displaystyle 5$ square feet, $3000ft^{2}\div5ft^{2}$ $\displaystyle 3000ft^{2}\div5ft^{2}$ per person = 600 $\displaystyle 600$ people

Flashcards: Extrapolating Linear Proportions

A cafeteria with $\displaystyle 40$ tables can sit 600 $\displaystyle 600$ people. Some tables can sit $\displaystyle 10$ people and some can sit $\displaystyle 20$ people. What is the ratio of the number of $\displaystyle 10$ -person tables to the number of $\displaystyle 20$ -person tables?

2:1 $\displaystyle 2:1$

1:1 $\displaystyle 1:1$

4:1 $\displaystyle 4:1$

1:2 $\displaystyle 1:2$

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Flashcards: Extrapolating Linear Proportions

Your answer:

2:1 $\displaystyle 2:1$

Your answer:

4:1 $\displaystyle 4:1$

Your answer:

1:2 $\displaystyle 1:2$

Correct answer:

1:1 $\displaystyle 1:1$

Explanation:

Let $\displaystyle x$ be the number of $\displaystyle 10$ -person tables, and $\displaystyle y$ be the number of $\displaystyle 20$ -person tables. Since there are $\displaystyle 40$ tables in the cafeteria, x+y=40 $\displaystyle x+y=40$ . 10x $\displaystyle 10x$ represents the number of people sitting at $\displaystyle 10$ -person tables, and 20y $\displaystyle 20y$ represents the number of people sitting at $\displaystyle 20$ -person tables. Since the cafeteria can seat 600 $\displaystyle 600$ people, $\displaystyle 10x+20y=600$ . Now we have $\displaystyle 2$ equations and $\displaystyle 2$ unknowns, and can solve the system. To do this, multiply the first equation by $\displaystyle 10$ and subtract it from the second equation. This yields $\displaystyle 0x+10y=200$ ; solving for $\displaystyle y$ tells us there are $\displaystyle 20$ tables that seat $\displaystyle 20$ people. Since x+y=40 $\displaystyle x+y=40$ , x=20 $\displaystyle x=20$ , so there are $\displaystyle 20$ tables that seat $\displaystyle 10$ people. The ratio of x:y $\displaystyle x:y$ is therefore 1:1 $\displaystyle 1:1$ .

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