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Algebraic equations are mathematical statements that express the equality between two algebraic expressions. When solving percent problems in algebra, we often translate the word problem into an equation. In our example, 48 is 15% of what number translates into the algebraic equation using the percent formula, which is written as rb = a. Here, r stands for the rate or percentage as a decimal, b is the base (the whole or original amount we are trying to find), and a is the amount that represents the given percentage of the base.

Understanding the relationship between these components is crucial because it helps to set up our equation properly. In our specific case, the equation 0.15 * b = 48 is derived where 0.15 is the decimal representation of 15%, b is the unknown we are aiming to solve for, and 48 is the known result of 15% of b. This expression is a simple linear equation and forms the foundation of many percent problems in algebra.

Percentage calculation involves finding a portion or a part of a whole number, expressed as a percentage. To solve percentage problems in algebra, it is essential to convert the percent to a decimal by dividing by 100, because the percent formula can only be applied with the rate in decimal form. For instance, 15% becomes 0.15. This conversion is a focal point in tackling percentage problems because it ensures that the multiplication within the algebraic equation correctly represents the proportionate amount.

Converting Percent to Decimal

Conversion from percent to decimal is done by simply moving the decimal point two places to the left. For example, to convert 15% to a decimal, you move the decimal point two places left, yielding 0.15. In our exercise, the percentage calculation is embedded within the equation itself, translating the percentage term into a solvable mathematical representation.

Isolating variables is a fundamental technique in algebra used to find the value of an unknown variable. When solving equations, one needs to manipulate the equation in such a way that the variable of interest is alone on one side of the equation. This process often involves performing the same operation on both sides of the equation to maintain equality.

To isolate the variable b in our equation 0.15 * b = 48, we divide both sides by 0.15. The operation is chosen to counteract the multiplication of b by 0.15, thus leaving b on its own on one side of the equation.

Dividing Both Sides

• Start with the equation: 0.15 * b = 48.
• Divide both sides by 0.15: b = 48 / 0.15.
• Simplify the division to find b.

After performing the operation, we find that b = 320. Isolating the variable is an essential skill that allows students to solve for unknown quantities not only in algebra but across all areas of mathematics.