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Chapter 5: Problem 29

Solve. $$ \frac{100}{25}=\frac{20}{n} $$

Short Answer

Expert verified
\(n = 5\)

Step by step solution

01

Cross Multiply

Cross multiply the given equation to create a new equation without fractions. This will give you:o\(\frac{100}{25} = \frac{20}{n} \)\(100 \times n = 25 \times 20\)
02

Simplify Both Sides

Simplify both sides of the equation. Calculate the products on each side:\(100n = 500\)
03

Solve for n

Divide both sides of the equation by 100 to isolate \(n\):\(\frac{100n}{100} = \frac{500}{100}\)\(n = 5\)

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Key Concepts

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

Cross Multiplication
Cross multiplication is an effective method to solve proportion problems. It helps eliminate fractions and makes equations more manageable. For instance, if you have an equation like \(\frac{100}{25}=\frac{20}{n}\), you can cross multiply to transform it into:
  • 100 \( \times \) * n = 25 \( \times \) * 20.
By doing this, you multiply diagonally across the equation, combining numerators and denominators. This results in a simple linear equation that is often easier to work with. The equation then becomes: \(100n = 500\), making it straightforward to solve.
Solving for Variables
Once you've cross multiplied and simplified both sides of the equation, the next step is to solve for the variable. In our example, the variable is 'n'. Once we have our equation: \(100n = 500\), we need to isolate 'n'. Here's how:
  • Divide both sides by 100 to isolate 'n'.
This simplifies to:\(\frac{100n}{100} = \frac{500}{100}\). The 100s cancel out on the left, leaving: \(n = 5\). This division approach helps isolate the unknown variable on one side, making it easy to identify its value.
Basic Algebra
Understanding basic algebra is crucial for solving proportion problems. Basic algebra involves working with variables and constants to form and solve equations. Here's a brief rundown of the essential steps we followed:
  • Identified the equation with fractions.
  • Used cross multiplication to remove the fractions.
  • Simplified both sides to form a linear equation.
  • Divided to isolate the variable 'n'.
Using basic algebraic principles, we identified the steps needed to solve the problem efficiently. Practicing these methods helps reinforce understanding and improves problem-solving skills.

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Most popular questions from this chapter

To measure the height of a hill, a string is stretched from level ground to the top of the hill. A 3 -ft stick is placed under the string, touching it at point \(P, \underline{a}\) distance of \(5 \mathrm{ft}\) from point \(G,\) where the string touches the ground. The string is then detached and found to be \(120 \mathrm{ft}\) long. How high is the hill?

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