# Lesson 5

Two Equations for Each Relationship

The practice problem answers are available at one of our IM Certified Partners

### Problem 1

The table represents the relationship between a length measured in meters and the same length measured in kilometers.

1. Complete the table.
2. 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
$$x$$

### 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 $$b =$$.

### 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.

1. How much does the nylon rope cost per meter?
2. How long is a piece of nylon rope that costs \$1.00?

### 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: $$y =$$

(From Grade7, Unit 2, Lesson 4.)

### Problem 5

On a map of Chicago, 1 cm represents 100 m.Select all statements that express the same scale.

A:

5 cm on the map represents 50 m in Chicago.

B:

1 mm on the map represents 10 m in Chicago.

C:

1 km in Chicago is represented by 10 cm the map.

D:

100 cm in Chicago is represented by 1 m on the map.

(From Grade7, Unit 1, Lesson 8.)