Write the equation that satisfies the parameters: three times the difference of a number and 10 equals the sum of 25 and that same number.

A) 3(x + 10) = 25 -x
B) 3x + 10 = 25 - x
C) 3x - 10 = 25 + x
D) 3(x + 10) = 25 + x

1 answer

To create an equation based on the given parameters "three times the difference of a number and 10 equals the sum of 25 and that same number," let's break this down step-by-step.

  1. Let the number be \(x\).
  2. The difference of the number and 10 is \(x - 10\).
  3. Three times this difference is \(3(x - 10)\).
  4. The sum of 25 and the same number is \(25 + x\).

Now we can set up the equation:

\[ 3(x - 10) = 25 + x \]

Next, we see if this matches any of the provided options. Let's rewrite the equation \( 3(x - 10) = 25 + x \):

  • Expanding \(3(x - 10)\): \[ 3x - 30 = 25 + x \]

We can rearrange it to find its equivalent form, but first, we can check the provided options directly:

A) \(3(x + 10) = 25 - x\)

B) \(3x + 10 = 25 - x\)

C) \(3x - 10 = 25 + x\)

D) \(3(x + 10) = 25 + x\)

Upon reviewing, none of the options directly match what we derived, but let's analyze them:

  1. Option A: \(3(x + 10) = 25 - x\) — This does not match.
  2. Option B: \(3x + 10 = 25 - x\) — This does not match.
  3. Option C: \(3x - 10 = 25 + x\) — This does not match.
  4. Option D: \(3(x + 10) = 25 + x\) — This does not match as well.

None of the options seem to match our derived equation \(3(x - 10) = 25 + x\). As the equation we constructed from the problem statement is technically correct, please double-check if there's a mistake in the problem statement or its interpretation.

If we strictly adhere to the problem as interpreted, none of the provided options are correct.