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Chapter 6: Problem 30

Translate to an equation and solve. \(70 \%\) of what is \(35 ?\)

Short Answer

Expert verified
The number is 50.

Step by step solution

01

- Understand the Problem

The problem asks you to find the number that, when multiplied by 70%, equals 35. This can be translated into an equation.
02

- Set Up the Equation

Let the unknown number be denoted as \( x \). The problem can be translated to the equation: \[ 0.70x = 35 \] where 0.70 represents 70%.
03

- Solve for \( x \)

To solve for \( x \), divide both sides of the equation by 0.70: \[ x = \frac{35}{0.70} \]
04

- Calculate the Result

Perform the division: \[ x = 50 \]
05

- Verify Your Answer

To verify, multiply 50 by 0.70 to ensure it equals 35: \[ 50 \times 0.70 = 35 \]. The calculation is correct, so \( x = 50 \).

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Key Concepts

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

Translating Word Problems
When faced with a word problem, the first step is to translate the words into mathematical language. In our exercise, we encounter the phrase: '70% of what is 35?'.
Understanding this phrase as a mathematical statement involves breaking it down:

  • '70%' translates to the decimal 0.70.
  • 'of what' suggests we are looking for an unknown value, which we can call \( x \).
  • 'is 35' means 'equals 35'.

So the original question can be rewritten as the equation: \( 0.70x = 35 \). This makes it easier to handle mathematically and sets us up for the next steps in solving the problem.
Setting Up Equations
Once we've translated the word problem into a mathematical equation, we need to lay out this equation properly to solve it. We've learned that '70% of what is 35?' translates to the equation: \( 0.70x = 35 \).
Here are the steps to set up and solve the equation:

  • Assign the unknown value to a variable. In this case, let that variable be \( x \).
  • Replace the words with their mathematical representations: '70%' becomes 0.70, and '35' remains 35.
  • Write out the equation based on these replacements: \( 0.70x = 35 \).

From here, it鈥檚 straightforward to isolate \( x \) by performing algebraic operations. Divide both sides by 0.70 to solve for \( x \). The division gives us: \( x = \frac{35}{0.70} \).
Verifying Solutions
After solving the equation, it's crucial to verify that our solution makes sense. For our example, we found \( x = 50 \) by solving \( x = \frac{35}{0.70} \).
To verify, we substitute \( x \) back into the original equation to check if the left side equals the right side:
  • Substitute 50 for \( x \) in \( 0.70x = 35 \).
  • Calculate \( 0.70 \times 50 \).
  • Check if this equals 35.

Performing the multiplication, \( 0.70 \times 50 = 35 \). Since both sides of the original equation balance, our solution \( x = 50 \) is correct. Always remember, verifying your answer is a crucial step to ensure accuracy in math problems.

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Most popular questions from this chapter

Simplify: \(4^{3}-6^{2} \div 2^{2}\)

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