Linear Equation Word Problems

A linear equation is an algebraic equation that represents a straight line when graphed on a Cartesian coordinate system.

It typically takes the form:

ax + by = c

where a, b, c are constants and x, y are variables.

The variables x and y each are raised to the power 1 and are not multiplied or divided by each other.

Linear equations can also be represented in slope-intercept form:

y = mx + b where m is the slope and b is the y-intercept.

Linear equation word problems involve real-world situations where relationships between variables can be described by linear equations. These problems require you to translate the given information into mathematical expressions and equations, solve them to find the unknowns, and then interpret the solutions in the context of the problem.

Example Questions

1. A car rental company charges a flat fee of $50 plus $20 per day for renting a car. Write a linear equation to represent the total cost (C) of renting a car for a certain number of days (d), and find the total cost for renting the car for 5 days.

Solution

Defining Variables:

Let:

C represents the total cost of renting the car.

d represents the number of days the car is rented.

Setting up the Equation:

We know that the total cost (C) consists of two parts: a flat fee of $50 and an additional charge of $20 per day. This can be represented by the equation:

C = 50 + 20d

This equation is linear because the relationship between the total cost and the number of days is a straight line.

Solving the Problem:

To find the total cost for renting the car for 5 days, we substitute d = 5 into the equation:

C = 50 + 2(5) = 50 + 100 = 150

So, the total cost for renting the car for 5 days is $150.

2. A fruit vendor sells apples for $2 each and oranges for $3 each. Write a linear equation to represent this and find the total cost of both 5 apples and 3 oranges.

Solution

Cost of each apple = c1 = $2

Cost of each orange = c2 = $3

Total cost of 5 apples and 3 oranges is given by the equation 5c1 + 3c2

= 5(2) + 3(3) = 10 + 9 = $19

3. Jane’s age is 5 years more than double the age of her brother. The sum of their ages is 35. How old are Jane and her brother?

Solution

Let j represent Jane’s age and b represent her brother’s age

According to the problem,

j = 2b + 5 ….(1) and

j + b = 35….(2)

Plugging j from (1) in (2)

(2b + 5) + b = 35

=> 3b = 30

=> b = 10

=> j = 35 – b = 35 – 10 = 25

4. Two third of a number is 8. Find the number.

Solution

Converting the statement into an equation, we have

2x/3 = 8

=> 2x = 24

x = 12

Linear Equation Word Problems FAQS

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