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Which algebraic equation represents the words:

Twenty percent of your grade is 80 points. What was your grade?

7 answers

To translate the words into an algebraic equation, let's define the variable:

Let \( x \) be your grade.

According to the information given, twenty percent of your grade (\( 0.20x \)) equals 80 points.

So, we can set up the equation:

\[ 0.20x = 80 \]

This equation represents the scenario given in the words.

.20x = 80

.20 = 80x

20x = 80

20/80 = x

Let's clarify and solve the equation step by step. Starting from the equation we derived:

\[ 0.20x = 80 \]

To isolate \( x \), we'll divide both sides of the equation by 0.20:

\[ x = \frac{80}{0.20} \]

Now we can calculate:

\[ x = \frac{80}{0.20} = 80 \div 0.20 = 80 \times 5 = 400 \]

So, your grade \( x \) is 400 points.

Now, you had the rearrangement .20 = 80x, which is incorrect. The correct steps lead to:

  1. Start with \( 0.20x = 80 \).
  2. Divide both sides by \( 0.20 \).
  3. Solve for \( x \).

The solution we found indicates that your grade is 400 points. If you have any further questions or if something isn't clear, feel free to ask!

which answer is it from what i pasted

Let's break down your pasted equations step-by-step to identify any issues and clarify the final result.

You started with:

  1. \( 0.20x = 80 \) (This was correct.)

You then wrote:

  1. \( 0.20 = 80x \) (This is incorrect; it changes the equation.)

Next, a rearrangement you had is:

  1. \( 20x = 80 \) (This could be correct if you multiply both sides of the original equation \( 0.20x = 80 \) by 100, but you didn't appropriately justify the switch.)

You then said:

  1. \( \frac{20}{80} = x \) (This is incorrect because it does not follow from your previous equations.)

The Correct Steps

Starting again from \( 0.20x = 80 \):

  1. Divide both sides by \( 0.20 \) to solve for \( x \):

    \[ x = \frac{80}{0.20} \]

  2. Calculate:

    \[ x = 80 \div 0.20 = 400 \]

So the final answer, your grade \( x \), is 400 points.

Summary

  • The correct equation is \( 0.20x = 80 \).
  • Solving this gives \( x = 400 \).
  • The steps you provided after the first statement are either improperly derived or incorrectly manipulated.

If you have further questions about any part of this, let me know!

which answer is correct?
.20x = 80

.20 = 80x

20x = 80

20/80 = x

Let's assess the equations you've listed, starting from the correct initial statement.

  1. Starting Equation: \[ 0.20x = 80 \]

  2. Incorrect Rearrangement: \[ 0.20 = 80x \]

    • This is incorrect because you cannot just rearrange the terms like that without maintaining the equality.

  3. Rearrangement: \[ 20x = 80 \]

    • This could be correctly derived if you multiply the first equation by 100, turning \( 0.20 \) into \( 20 \).

  4. Incorrect Final Statement: \[ \frac{20}{80} = x
    \]

    • This is incorrect; it does not follow from \( 20x = 80 \).

Correct Steps from \( 0.20x = 80 \):

To find \( x \):

  1. Start with: \[ 0.20x = 80 \]

  2. Divide both sides by \( 0.20 \): \[ x = \frac{80}{0.20} \]

  3. Calculate \( \frac{80}{0.20} \): \[ x = 400 \]

Summary of Correctness:

  • The correct first equation is \( 0.20x = 80 \).
  • When rearranged properly, it leads to \( x = 400 \).
  • The statements \( 0.20 = 80x \) and \( \frac{20}{80} = x \) are incorrect manipulations.

Thus, the correct outcome is that your grade \( x = 400 \). If you only want to focus on which of your statements is correct, begin with \( 0.20x = 80\), and from there, proceed correctly to find \( x \). If you multiply to eliminate the decimal, you can get to \( 20x = 80 \), which can be solved to find \( x \), but it must be done correctly by following appropriate algebraic steps.