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The percentage formula is a foundational concept in mathematics that helps in determining what part of a whole a number represents, expressed as a percentage. The generic formula is:\[ \text{{percentage}} = \frac{{\text{{part}}}}{{\text{{whole}}}} \times 100 \]Here, the 'part' is the portion of the 'whole' you're focused on. For example, if you have a part of 25 and a whole of 100, your percentage is 25%.In our exercise, we aim to find out what number (the whole) 11.5% of it makes up \( 108.10 \). To set up this equation, we can rearrange the formula to solve for the whole:\[ \text{{whole}} = \frac{{\text{{part}} \times 100}}{{\text{{percentage}}}} \]Inserting our known values, we get:\[ x = \frac{{108.10 \times 100}}{{11.5}} \]This equation helps us find the unknown by isolating it through algebra, a crucial step when translating word problems into mathematical equations.

Solving for \( x \) involves isolating the variable to find its value. In our scenario, we set up the equation as:\[ \frac{{108.10}}{{x}} \times 100 = 11.5 \]First, we rearrange it to isolate \( x \):\[ 108.10 \times 100 = 11.5x \]Next, we perform the multiplication on the left side:\[ 10810 = 11.5x \]To solve for \( x \), we divide both sides by 11.5: \[ x = \frac{{10810}}{{11.5}} \]Here, we focus on basic algebraic operations like multiplication and division to find the value of \( x \), which simplifies our problem.Performing the division, we get:\[ x = 940 \]Thus, the number for which 11.5% is 108.10 is 940.

Basic algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols. In most cases, we're solving equations to find the value of unknown variables. Key operations include:

• Addition
• Subtraction
• Multiplication
• Division

Consider our problem:\[ \frac{{108.10}}{{x}} \times 100 = 11.5 \]We use multiplication and division to isolate \( x \). First, we multiply both sides by \( x \):\[ 108.10 \times 100 = 11.5x \]This step eliminates \( x \) from the denominator. Next, we divide both sides by 11.5 to solve for \( x \):\[ x = \frac{{10810}}{{11.5}} \]These steps illustrate the importance of basic algebraic principles in solving percentage problems. Being comfortable with these operations makes solving more complex problems easier.