Lesson 2
Two Equations for Each Relationship
Problem 1
The table represents the relationship between a length measured in meters and the same length measured in kilometers.
- Complete the table.
- Write an equation for converting the number of meters to kilometers. Use x for number of meters and y for number of kilometers.
meters | kilometers |
---|---|
1,000 | 1 |
3,500 | |
500 | |
75 | |
1 | |
x |
Solution
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Problem 2
Concrete building blocks weigh 28 pounds each. Using b for the number of concrete blocks and w for the weight, write two equations that relate the two variables. One equation should begin with w = and the other should begin with b =.
Solution
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Problem 3
A store sells rope by the meter. The equation p = 0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long.
- How much does the nylon rope cost per meter?
- How long is a piece of nylon rope that costs $1.00?
Solution
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Problem 4
The table represents a proportional relationship. Find the constant of proportionality and write an equation to represent the relationship.
a | y |
---|---|
2 | \frac23 |
3 | 1 |
10 | \frac{10}{3} |
12 | 4 |
Constant of proportionality: __________
Equation: y =
Solution
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(From Unit 5, Lesson 1.)Problem 5
Jada walks at a speed of 3 miles per hour. Elena walks at a speed of 2.8 miles per hour. If they both begin walking along a walking trail at the same time, how much farther will Jada walk after 3 hours? Explain your reasoning.
Solution
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(From Unit 2, Lesson 18.)