Lesson 6
Using Equations to Solve Problems
Let’s use equations to solve problems involving proportional relationships.
Problem 1
A car is traveling down 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?
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?
Problem 3
There are about 1.61 kilometers in 1 mile. Let \(x\) represent a distance measured in kilometers and \(y\) represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles.
Problem 4
In Canadian coins, 16 quarters is equal in value to 2 toonies.
number of quarters | number of toonies |
---|---|
1 | |
16 | 2 |
20 | |
24 |
- Complete the table.
- What does the value next to 1 mean in this situation?
Problem 5
Each table represents a proportional relationship. For each table:
- Fill in the missing parts of the table.
- 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 notice in two polygons that would help you decide that they were not scaled copies.