Let's break down the statement: "three times the difference of a number and 10 equals the sum of 25 and that same number."
First, we'll define the variable:
- Let \( x \) be the number.
The phrase "the difference of a number and 10" can be expressed as \( x - 10 \).
Next, "three times the difference" means we need to multiply that difference by 3: \[ 3(x - 10) \]
Now, the statement says this is equal to "the sum of 25 and that same number": \[ 25 + x \]
Putting it all together, we have the equation: \[ 3(x - 10) = 25 + x \]
Now, let's look at the options provided:
A) \( 3(x + 10) = 25 - x \)
B) \( 3x + 10 = 25 - x \)
C) \( 3x - 10 = 25 + x \)
D) \( 3(x - 10) = 25 + x \)
The correct answer is: D) \( 3(x - 10) = 25 + x \)