Problem 39 - Algebra for College Students

Question

Solve each problem. In \(2017,\) two popular brands on Instagram were National Geographic and Nike. National Geographic had 8.0 million more followers than Nike. Together, the two brands had 158.8 million followers. How many followers did each brand have?

Step-by-Step Solution

Answer

Nike had 75.4 million followers, and National Geographic had 83.4 million followers.

Step 1: Set up variables

Let the number of followers Nike had be represented by the variable \( x \). Since National Geographic had 8.0 million more followers than Nike, we can represent the followers of National Geographic by \( x + 8 \).

Step 2: Write the equation

Together, the two brands had 158.8 million followers. This setup can be written using the equation: \( x + (x + 8) = 158.8 \).

Step 3: Simplify the equation

Combine the terms to simplify the equation: \( x + x + 8 = 158.8 \) becomes \( 2x + 8 = 158.8 \).

Step 4: Solve for x

Isolate the variable \( x \). Subtract 8 from both sides: \( 2x = 150.8 \). Then divide by 2: \( x = 75.4 \). This means Nike had 75.4 million followers.

Step 5: Find the followers for National Geographic

Use the value of \( x \) to find the followers of National Geographic. Since it had 8 million more followers than Nike: \( 75.4 + 8 = 83.4 \). National Geographic had 83.4 million followers.

Key Concepts

variables in algebra

In algebra, variables are symbols used to represent unknown values. When solving real-world problems, we assign variables to these unknowns to help set up equations. For example, in the exercise, we let the variable \( x \) represent the number of followers Nike had on Instagram. By assigning this variable, we can easily work through the problem step-by-step to find the solution.

combining like terms

Combining like terms is a crucial technique in simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. For example, \( x \) and \( 2x \) are like terms, but \( x \) and \( x^2 \) are not. In the exercise, we had the equation \( x + (x + 8) = 158.8 \). When we simplified it by combining like terms, \( x + x \) became \( 2x \). This simplification makes it easier to solve the equation.

solving for x

Solving for \( x \) means isolating the variable on one side of the equation to find its value. In the exercise, after combining like terms, we had the simplified equation \( 2x + 8 = 158.8 \). To isolate \( x \), we subtracted 8 from both sides, resulting in \( 2x = 150.8 \). Then, we divided both sides by 2 to get \( x = 75.4 \). This process of isolating \( x \) involves inverse operations, such as subtraction and division, to undo the operations applied to \( x \).

linear equations

Linear equations are equations of the first degree, meaning they have variables raised to the power of one. These equations form a straight line when graphed. In our exercise, we dealt with the linear equation \( x + x + 8 = 158.8 \), which simplifies to \( 2x + 8 = 158.8 \). Solving linear equations typically involves combining like terms and using inverse operations to isolate the variable. These solutions help us understand and solve real-world problems efficiently.