Unit 4, Lesson 3
Writing Equations to Model Relationships (Part 2)
Integrated Math 1
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Here is a table of values. The two quantities, and , are related.
| 1 | 0 |
| 3 | 8 |
| 5 | 24 |
| 7 | 48 |
What are some strategies you could use to find a relationship between and ? Brainstorm as many ways as possible.
Describe in words how the two quantities in each table are related.
| number of laps, | 0 | 1 | 2.5 | 6 | 9 |
|---|---|---|---|---|---|
| meters run, | 0 | 400 | 1,000 | 2,400 | 3,600 |
| meters from home, | 0 | 75 | 128 | 319 | 396 |
|---|---|---|---|---|---|
| meters from school, | 400 | 325 | 272 | 81 | 4 |
| electricity bills in dollars, | 85 | 124 | 309 | 816 |
|---|---|---|---|---|
| total expenses in dollars, | 485 | 524 | 709 | 1,216 |
| monthly salary in dollars, | 872 | 998 | 1,015 | 2,110 |
|---|---|---|---|---|
| amount deposited in dollars, | 472 | 598 | 615 | 1,710 |
Match each table to an equation that represents the relationship.
| base length (inches) | height (inches) |
|---|---|
| 1 | 48 |
| 2 | 24 |
| 3 | 16 |
| 4 | 12 |
| 6 | 8 |
Visitors to a carnival are invited to guess the number of beans in a jar. The person who guesses the correct number wins \$300. If multiple people guess correctly, the prize will be divided evenly among them.
What is the relationship between the number of people who guess correctly and the amount of money each person will receive?
A -gallon jug of milk can fill 8 cups, while 32 fluid ounces of milk can fill 4 cups.
What is the relationship between the number of gallons and ounces? If you get stuck, try creating a table.
Sometimes, the relationship between two quantities is easy to see. For instance, we know that the perimeter of a square is always 4 times the side length of the square. If represents the perimeter and represents the side length, then the relationship between the two measurements (in the same unit) can be expressed as , or .
Other times, the relationship between quantities might take a bit of work to figure out—by doing calculations several times or by looking for a pattern. Here are two examples.
| miles from New Orleans | miles from San Diego |
|---|---|
| 100 | 1,500 |
| 300 | 1,300 |
| 500 | 1,100 |
| 1,020 | |
| 900 | 700 |
| 1,450 | |
What is the relationship between the two distances? Do you see any patterns in how each quantity is changing? Can you find out what the missing values are?
Notice that every time the distance from New Orleans increases by some number of miles, the distance from San Diego decreases by the same number of miles, and that the sum of the two values is always 1,600 miles.
The relationship can be expressed with any of these equations:
A company decides to donate \$50,000 to charity. It will select up to 20 charitable organizations, as nominated by its employees. Each selected organization will receive an equal amount of donation.
What is the relationship between the number of selected organizations, , and the dollar amount each of them will receive, ?
If 20 organizations are selected, each one receives \$2,500.
Do you notice a pattern here? 10,000 is , 5,000 is , and 2,500 is .
We can generalize that the amount each organization receives is 50,000 divided by the number of selected organizations, or .