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# Variable Expressions

## Letters representing numbers in arithmetic expressions

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Practice Variable Expressions

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Planets
Teacher Contributed

## Real World Applications – Algebra I

### Topic

How can we represent how long it takes planets to orbit the sun?

### Student Exploration

#### Have you thought about how long it takes all nine planets to orbit the sun?

Let’s first take a look at planet earth.

1. If we have no idea how long it takes our planet to orbit the sun, and we want to represent the number of days it takes to orbit the sun, how can we represent this unknown as a variable? Which variable would you choose, and why? What would it represent, in your own words?
2. It takes the planet Jupiter 12 times longer than the earth to orbit the sun. How could you represent this relationship as an expression?
1. It takes Saturn 29 times longer than the earth to orbit the sun. What is the expression to represent this relationship?
2. It takes Uranus 84 times longer than the earth to orbit the sun. What is the expression to represent this relationship?
3. It takes Neptune 165 times longer than the earth to orbit the sun. What is the expression to represent this relationship?
4. It takes Mars about 1.877 times longer than the earth to orbit the sun. What is the expression to represent this relationship?
3. If we just found out that it takes the earth to orbit the sun 365 days, find out how many days it takes for Jupiter, Saturn, Uranus, Neptune and Mars to orbit the sun.
4. It takes Venus 225 days to orbit the sun. What expression could we use to describe how fast its orbit is in relation to the earth?
1. It takes Mercury 88 days to orbit the sun. How much faster does it rotate the sun in comparison to the earth?

### Extension Investigation

1. In the questions above, we used the earth as the unknown quantity and related all of the other planets’ speed of rotation around the sun to the earth. What if all of the planets rotated around how fast Mercury’s rotation around the sun? How would the numbers change? What units would you use?

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