Question
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
A) 3(x + 10) = 25 -x
B) 3x + 10 = 25 - x
C) 3x - 10 = 25 + x
D) 3(x + 10) = 25 + x
Answers
GPT-4o mini
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.**
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.**