Unit 2, Lesson 6
Writing Equations to Represent Relationships
Grade 7
Practice
Problem 1
A car is traveling on a highway at a constant speed, described by the equation \(d = 65t\), where \(d\) represents the distance, in miles, that the car travels at this speed in \(t\) hours.
- What does the 65 tell us in this situation?
- How many miles does the car travel in 1.5 hours?
- How long does it take the car to travel 26 miles at this speed?
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Problem 2
Elena has some bottles of water that each holds 17 fluid ounces.
- Write an equation that relates the number of bottles of water (\(b\)) to the total volume of water (\(w\)) in fluid ounces.
- How much water is in 51 bottles?
- How many bottles does it take to hold 51 fluid ounces of water?
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Problem 3
There are about 1.61 kilometers in 1 mile. Use \(x\) to represent a distance measured in kilometers and \(y\) to represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles.
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In Canadian coins, 16 quarters is equal in value to 2 toonies.
- Complete the table.
- What does the value in the right column that is next to 1 in the left column mean in this situation?
| number of quarters | number of toonies |
|---|---|
| 1 | |
| 16 | 2 |
| 20 | |
| 24 |
Each table represents a proportional relationship. For each table:
- Fill in the unknown values.
- Draw a circle around the constant of proportionality.
| \(x\) | \(y\) |
|---|---|
| 2 | 10 |
| 15 | |
| 7 | |
| 1 |
| \(a\) | \(b\) |
|---|---|
| 12 | 3 |
| 20 | |
| 10 | |
| 1 |
| \(m\) | \(n\) |
|---|---|
| 5 | 3 |
| 10 | |
| 18 | |
| 1 |
Problem 6
Describe some things you could observe about two polygons that would help you decide that they were not scaled copies.
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