Question

equations of proportional relationships practice

Answer 1

Proportional relationships can be expressed using equations of the form \( y = kx \), where \( k \) is the constant of proportionality, \( y \) is the dependent variable, and \( x \) is the independent variable. Here are some practice problems involving proportional relationships:

### Practice Problems

**Problem 1:**
A car travels 60 miles in 1 hour. Write the equation that represents the relationship between the distance traveled \( d \) (in miles) and the time \( t \) (in hours).

**Problem 2:**
A recipe requires 2 cups of flour to make 12 cookies. Write an equation that describes the relationship between the number of cookies \( c \) and the cups of flour \( f \) used.

**Problem 3:**
A painter charges $20 per hour for his work. Write the equation for the relationship between the total cost \( C \) (in dollars) and the number of hours worked \( h \).

**Problem 4:**
A truck can carry 500 pounds of cargo. If it carries a certain amount of cargo, write an equation to describe the relationship between the weight of cargo \( w \) (in pounds) and the number of trips \( t \) made if one trip carries the full 500 pounds.

**Problem 5:**
The rental cost of a bike is $5 per hour. Write the equation for the relationship between the rental cost \( R \) (in dollars) and the number of hours \( h \) the bike is rented.

### Answers

**Answer 1:**
The equation is \( d = 60t \).

**Answer 2:**
The equation is \( f = \frac{1}{6}c \) (because \( 2 \) cups of flour make \( 12 \) cookies, so \( f = \frac{2}{12}c = \frac{1}{6}c \)).

**Answer 3:**
The equation is \( C = 20h \).

**Answer 4:**
The equation is \( w = 500t \).

**Answer 5:**
The equation is \( R = 5h \).

Feel free to create more problems based on these formats, or modify these examples to suit different contexts!