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Chapter 2: Problem 93

Solve each problem. \(42 \%\) of what number is \(294 ?\)

Short Answer

Expert verified
The number is 700.

Step by step solution

01

- Understand the Problem

We need to find out what number, when 42% of it is taken, results in 294.
02

- Define the Variables

Let the unknown number be denoted by \(x\). Therefore, 42% of \(x\) can be expressed as \(0.42x\).
03

- Set Up the Equation

According to the problem, 42% of \(x\) equals 294. Therefore, we can set up the equation: \(0.42x = 294\).
04

- Solve for x

To find \(x\), we need to isolate it by dividing both sides of the equation by 0.42: \[ x = \frac{294}{0.42} \]
05

- Calculate the Result

Perform the division to get the value of \(x\): \[ x = 700 \]

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Key Concepts

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

algebraic equation
An algebraic equation is a mathematical statement that shows the equality of two expressions. In our problem, we have the equation: \(0.42x = 294\). This equation conveys that 42% of some number, represented by \(x\), equals 294. Equations are crucial in mathematics because they allow us to find unknown values by applying certain rules and operations.
solving for a variable
Solving for a variable means finding the value of that variable that makes the equation true. In our exercise, we need to find the value of \(x\). To do this, we isolate \(x\) on one side of the equation. Starting with \(0.42x = 294\), we divide both sides of the equation by 0.42. This gives us:
  • \( x = \frac{294}{0.42} \)
Isolating the variable allows us to find its specific value.
dividing decimals
Dividing decimals can be tricky, but with practice, it becomes more manageable. In this problem, we need to divide 294 by 0.42 to solve for \(x\). Here's how we can do it step-by-step:
  • First, move the decimal point in the divisor (0.42) to the right until it is a whole number. Here, we move it two places to get 42.
  • Do the same with the dividend (294), moving the decimal point two places to get 29400.
  • Now, divide 29400 by 42. Performing the division, we find that \(x = 700\).
Breaking down the process makes dividing decimals more straightforward.

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Most popular questions from this chapter

Two angles whose measures sum to \(90^{\circ}\) are \(\longrightarrow\) angles. Two angles whose measures sum to \(180^{\circ}\) are \(\longrightarrow\) angles.

Find the measure of an angle whose complement is four times its measure. (Hint: If \(x\) represents the measure of the unknown angle, how would we represent its complement?)

Graph the solution set, and write it using interval notation \(-12 \leq \frac{1}{2} z+1 \leq 4\)

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