/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 Solve \(\frac{R}{2}+\frac{W}{5}=... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 43

Solve \(\frac{R}{2}+\frac{W}{5}=21\) for \(R\)

Short Answer

Expert verified
R = 42 - \(\frac{2W}{5}\)

Step by step solution

01

Isolate the term with R

Subtract \(\frac{W}{5}\) from both sides of the equation to isolate the term with \(R\). The equation becomes \(\frac{R}{2} = 21 - \frac{W}{5}\).
02

Remove the fraction

Multiply both sides of the equation by 2 to get rid of the fraction on the left side. This gives us \(R = 2 \times (21 - \frac{W}{5})\).
03

Distribute on the right side

Distribute the 2 on the right side of the equation: \(R = 2 \times 21 - 2 \times \frac{W}{5}\), which simplifies to \(R = 42 - \frac{2W}{5}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables
When solving linear equations, isolating the variable you are solving for is a key step. You want to get the variable on one side of the equation by itself. Here, we are solving for \(R\).
First, notice the equation \(\frac{R}{2} + \frac{W}{5} = 21\). To isolate \(R\), you need to remove \(\frac{W}{5}\) from the left side. You can do this by subtracting \(\frac{W}{5}\) from both sides of the equation. This process ensures the equation remains balanced.
The equation then looks like this: \(\frac{R}{2} = 21 - \frac{W}{5}\). Now, \(R\) is isolated to one side of the equation, making it easier to solve.
Fraction Operations
Working with fractions in equations can be tricky, but understanding the operations helps. In our step-by-step solution, we first subtracted \(\frac{W}{5}\) from both sides to isolate \(R\). Understand that fractions follow the same principles as whole numbers but require careful handling:
  • Add or subtract fractions with the same denominator directly
  • For fractions with different denominators, find a common denominator first
  • To clear a fraction from one side of an equation, multiply every term by the denominator

In our equation, after isolating \(R\), we need to eliminate the fraction \(\frac{R}{2}\). We do this by multiplying both sides by the denominator, 2. This step clears the fraction and simplifies further calculations. The new equation becomes \(R = 2 \times (21 - \frac{W}{5})\).
Distributive Property
The distributive property helps in simplifying equations, especially when dealing with expressions inside parentheses. It states that \(a(b + c) = ab + ac\).
Applying this to our equation \(R = 2 \times (21 - \frac{W}{5})\), we distribute the 2 to both terms inside the parentheses:\(R = 2 \times 21 - 2 \times \frac{W}{5}\). Simplifying this, we get \(R = 42 - \frac{2W}{5}\).Now, we have our final solution, where \(R\) is expressed in terms of \(W\) and constants. Distributing is useful in breaking down expressions into simpler, more manageable parts.
Always remember to distribute correctly to avoid errors in your final equation.

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