Examples on Coefficient of a Variable

Some of the examples on Coefficient of Variable are discussed below:

Example 1: In the expression 5x-2y+3z, what are the coefficients of x, y, and z?

Solution:

In the expression 5x – 2y + 3z, the coefficients are as follows:

• Coefficient of x: Coefficient of x is the number directly multiplied by x, which is 5.

• Coefficient of y: Coefficient of y is the number directly multiplied by y, which is -2. (Note: Coefficients can be negative.)

• Coefficient of z: Coefficient of z is the number directly multiplied by z, which is 3.

So, coefficients of x, y, and z are 5, -2, and 3 respectively.

Example 2: A company produces two types of products, A and B. The profit from selling each unit of product A is $3, and the profit from selling each unit of product B is $5. If the company sells x units of product A and y units of product B, write an expression to represent the total profit.

Solution:

To represent the total profit, we need to multiply the number of units sold for each product by their respective profits and then sum the results.

Here’s the expression:

Total profit = (3x + 5y)

Expression represents the profit from selling (x) units of product A, each yielding $3 profit, and (y) units of product B, each yielding $5 profit.

Suppose the company sells 10 units of product A (x = 10) and 15 units of product B (y = 15).

Putting these values into the expression:

Total profit = (3 × 10 + 5 × 15)

= (30 + 75)

= 105

So, if the company sells 10 units of product A and 15 units of product B, the total profit would be $105.

Example 3: Solve the equation 2x + 4 = 10 to find the value of x.

Solution:

To solve the equation 2x + 4 = 10 for x, follow these steps:

Isolate the variable term: Subtract 4 from both sides of the equation to isolate the term containing x:

2x + 4 − 4 = 10−4

2x = 6

Solve for x: Divide both sides by 2 to solve for x:

2x/3 = 6/2

x = 3

So, the value of x that satisfies the equation 2x + 4 = 10 is x = 3.

The coefficient of a variable is a number that is multiplied by a variable in an algebraic expression. It’s often a constant that represents the number of units of the variable.

Coefficient in Math is a number or alphabet or a symbol multiplied by a variable in an algebraic expression, showing the variable’s impact on the expression. For example, in the expression 4xy, the coefficient in 4 which is multiplied by the variable xy.

In this article, we will understand the meaning of a coefficient, the properties of a coefficient, the types of coefficients, how to find a coefficient, and the difference between a coefficient and a constant.