Word problems are a great way to apply mathematical concepts in real-life scenarios. When it comes to linear equations, word problems can help students understand how to represent and solve problems using algebraic expressions. Here, we will explore some common word problems for linear equations that can be used in a worksheet to practice solving equations.
Linear equations are equations that represent a straight line when graphed. They have the general form of y = mx + b, where m is the slope of the line and b is the y-intercept. Word problems for linear equations often involve finding the relationship between two variables and using that information to solve for an unknown value. These problems can be challenging but are essential for developing problem-solving skills in algebra.
Word Problems for Linear Equations Worksheet
1. Sally is twice as old as her sister. The sum of their ages is 36. How old is each sister?
To solve this problem, we can set up two equations:
Let x be the age of Sally’s sister and 2x be Sally’s age.
x + 2x = 36
3x = 36
x = 12
Sally’s sister is 12 years old, and Sally is 24 years old.
2. A car rental company charges a flat fee of $30 plus $0.25 per mile driven. If a customer’s bill is $55, how many miles did they drive?
Let x be the number of miles driven.
0.25x + 30 = 55
0.25x = 25
x = 100
The customer drove 100 miles.
3. A bakery sells muffins for $1 each and cookies for $2 each. If they sell 50 items for $75, how many of each item did they sell?
Let x be the number of muffins sold and y be the number of cookies sold.
x + y = 50
x + 2y = 75
Substitute the first equation into the second equation:
50 + 2y = 75
2y = 25
y = 12.5 (rounded to 13)
x = 50 – 13 = 37
The bakery sold 37 muffins and 13 cookies.
Word problems for linear equations provide valuable practice in applying algebraic concepts to real-world situations. By working through these problems, students can improve their problem-solving skills and gain a better understanding of how to represent and solve linear equations. Incorporating these word problems into a worksheet can help reinforce these concepts and prepare students for more complex algebraic problems in the future.