91Ó°ÊÓ

Understanding how to convert percentages to decimals is crucial in solving percent problems in algebra. Percentages represent a part of a whole, where the whole is typically considered to be 100. To convert from a percentage to a decimal, simply divide by 100, which moves the decimal point two places to the left. For instance, \(70\text{%}\) becomes \(0.70\) after conversion.

This is because the word 'percent' itself means 'per hundred'. Thus, \(70\text{%}\) can be literally read as \(70\) per \(100\), or \(70/100\), which simplifies to \(0.7\). This conversion is the first crucial step in setting up equations involving percentages.

Linear equations are fundamental in algebra, representing a straight-line relationship between variables. When you're faced with a linear equation like \(0.7*x = 224\), the goal is to isolate and solve for the unknown variable, which in this case is \(x\). To do this, perform the same operation on both sides of the equation to maintain equality.

If you divide both sides of the equation by \(0.7\), you're effectively doing the reverse operation of multiplication, bringing you closer to the value of \(x\). This leaves \(x = 224 / 0.7\). This technique is not just about manipulation of numbers, but also about understanding the balance and structure of equations. Every step in solving a linear equation should bring you closer to finding out what the unknown variable equals.

When dealing with percent problems, it's important to clearly distinguish between the 'part' and the 'whole'. The 'whole' is the initial quantity you're considering, while the 'part' is a portion of that whole. In the context of our exercise, \(224\) represents the 'part', since it's the result of 70% of the 'whole' we're looking to find.

In percentages, the 'whole' is often represented by 100% or the entirety of something. In this case, the 'whole' is the unknown 'x', and it is what we aim to discover through our algebraic equation. Knowing which numbers represent parts and wholes is key to setting up your equation correctly and applying the right operations to find your answer.