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.
- Let the number be \(x\).
- The difference of the number and 10 is \(x - 10\).
- Three times this difference is \(3(x - 10)\).
- 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:
- Option A: \(3(x + 10) = 25 - x\) — This does not match.
- Option B: \(3x + 10 = 25 - x\) — This does not match.
- Option C: \(3x - 10 = 25 + x\) — This does not match.
- 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.