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Chapter 7: Problem 93

$$ \text { Solve: } 800=5 k $$

Short Answer

Expert verified
The value of \(k\) is 160.

Step by step solution

01

- Isolate the Variable

To find the value of the variable \(k\), we need to isolate it on one side of the equation. The given equation is \(800 = 5k\).
02

- Divide Both Sides by 5

To isolate \(k\), divide both sides of the equation by 5. This gives us \(k = \frac{800}{5}\).
03

- Simplify the Right-Hand Side

Perform the division to simplify the right-hand side of the equation: \(k = 160\).

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Key Concepts

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

Isolate the Variable
In solving linear equations, the first step is often to isolate the variable. This simply means getting the variable by itself on one side of the equation.
For example, let's consider our equation: \( 800 = 5k \).
Here, we want to solve for \( k \). To do this, we need \( k \) to appear alone on one side of the equation, with no other coefficients or constants attached to it.
The 'isolate the variable' step helps us simplify the problem and makes it easier to find the solution.
Division Property of Equality
The division property of equality is used when the variable you are solving for is multiplied by a coefficient. This principle states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.
In our problem, we started with \( 800 = 5k \).
To isolate \( k \), we divide both sides by 5:
  • Left Side: \( \frac{800}{5} \)
  • Right Side: \( \frac{5k}{5} \)
This leads us to the simplified equation \( k = 160 \).
It's important to always perform the same operation on both sides to maintain the balance of the equation.
Simplification
Simplification is the process of performing mathematical operations to make an equation easier to understand and solve.
After dividing both sides in our equation by 5, we got \( k = \frac{800}{5} \).
The final step is to perform the actual division to simplify this expression.
In this case, \( \frac{800}{5} = 160 \).
Thus, we conclude that \( k = 160 \).
Simplification helps to get the final, user-friendly answer that is easy to interpret.

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Most popular questions from this chapter

For exercises \(67-82\), use the five steps and a proportion. In 2010 , there were \(14.9\) cases of syphilis per 100,000 Americans with a total of 45,834 cases of syphilis. Find the population of Americans used to create this ratio. Round to the nearest hundred. (Source: www.cdc.gov, 2011)

The relationship of \(x\) and \(y\) is a direct variation. When \(x=1, y=5\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this direct variation. c. Find \(y\) when \(x=2\). d. Use slope-intercept graphing to graph this equation. e. Use the graph to find \(y\) when \(x=3\).

For exercises \(67-82\), use the five steps and a proportion. About five of 100 pregnant women have pre-eclampsia, a condition that results in high blood pressure. About 300,000 pregnant women per year in the United States have pre-eclampsia. Find the number of pregnant women in the United States used to create this ratio. (Source: www.nytimes.com, March 17, 2009)

The relationship of \(x\) and \(y\) is an inverse variation. When \(x=3, y=6\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this inverse variation. c. Find \(y\) when \(x=9\).

Find the number of 80,500 children and adolescents who are obese. Round to the nearest hundred. Approximately one in six children and adolescents are obese. (Source: www.cdc.gov, Nov. 2011)
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