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Chapter 6: Problem 106

Translate and solve. 28 is 25% of what number?

Short Answer

Expert verified
The number is 112.

Step by step solution

01

Identify the variables

Let the unknown number be represented by the variable \(x\).
02

Set up the equation

Translate the statement '28 is 25% of what number?' into an equation. Since 25% can be written as \(\frac{25}{100}\) or \(0.25\), the equation is: \[ 28 = 0.25 \times x \]
03

Solve the equation

To find \(x\), divide both sides of the equation by 0.25: \[ x = \frac{28}{0.25} \]
04

Perform the division

Calculate the right-hand side: \[ x = 112 \]

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Key Concepts

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

translate word problems into equations
Translating word problems into equations is key to solving math problems
efficiently and accurately. In this exercise, we start with a sentence: '28 is 25% of what number?'
To turn this into an equation:
  • Identify the important pieces: 28, 25%, and the unknown number, which we'll call x.
  • Translate 25% to its decimal form: 25% = 0.25.
  • Combine these into an equation: 28 = 0.25 x.
This approach helps us turn words into mathematical symbols and operations,
making it much easier to solve the problem step-by-step.
solving equations with percentages
Solving equations with percentages involves several key steps.
Let's go back to our equation: 28 = 0.25 x.
To isolate x, we need to get rid of the 0.25 that's multiplying it. We do this
by dividing both sides of the equation by 0.25:
  • On the left side, we have 28 梅 0.25.
  • On the right side, 0.25 梅 0.25 equals 1, so we're left with just x.
Thus, we rewrite the equation as: x = 28 梅 0.25
Now, we can move on to solve this division.
basic division in word problems
To solve the equation x = 28 梅 0.25, we need to perform the division.
Here's how we can do it:
  • Set up the division problem: 28 梅 0.25.
  • Convert 0.25 into a fraction to simplify the division. 0.25 as a fraction is 1/4.
  • Dividing by a fraction is the same as multiplying by its reciprocal. So, 28 梅 0.25
    is the same as 28 x 4.
Perform the multiplication: 28 x 4 = 112
Therefore, x = 112.
Always check your work: 0.25 times 112 should equal 28, confirming our solution.

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Most popular questions from this chapter

Hernando's salary was \(\$ 49,500\) last year. This year his salary was cut to \(\$ 44,055\) . Find the percent decrease.

In the following exercises, solve the percent problem. Kiyoshi bought a television set on sale for \(\$ 899\) . The original price was \(\$ 1,200\) . Find: (a) the amount of discount (b) the discount rate (round to the nearest tenth of a percent)

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In the following exercises, solve the percent problem. The total number of vehicles on one freeway dropped from \(84,000\) to \(74,000\) . Find the percent decrease (round to the nearest tenth of a percent).

Ayodele got a raise in her hourly pay, from \(\$ 24.50\) to \(\$ 25.48 .\) Find the percent increase.
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