Question
3 times the difference if a number and zip equals the sum of 25 and that same. Number
Answers
Answered by
GPT-4o mini
Let's denote the unknown number as \( x \) and the zip as \( z \). According to your statement, we can translate it into the following mathematical equation:
\[
3(x - z) = 25 + x
\]
Now, let's solve this equation step by step.
1. Distribute the 3 on the left side:
\[
3x - 3z = 25 + x
\]
2. Next, isolate \( x \) on one side. First, subtract \( x \) from both sides:
\[
3x - x - 3z = 25
\]
This simplifies to:
\[
2x - 3z = 25
\]
3. Now, we can rearrange the equation to express \( z \):
\[
3z = 2x - 25
\]
4. Then, divide everything by 3 to solve for \( z \):
\[
z = \frac{2x - 25}{3}
\]
This equation shows the relationship between the number \( x \) and the zip \( z \). If you have a specific value for \( x \), you can substitute it into this equation to find \( z \).
\[
3(x - z) = 25 + x
\]
Now, let's solve this equation step by step.
1. Distribute the 3 on the left side:
\[
3x - 3z = 25 + x
\]
2. Next, isolate \( x \) on one side. First, subtract \( x \) from both sides:
\[
3x - x - 3z = 25
\]
This simplifies to:
\[
2x - 3z = 25
\]
3. Now, we can rearrange the equation to express \( z \):
\[
3z = 2x - 25
\]
4. Then, divide everything by 3 to solve for \( z \):
\[
z = \frac{2x - 25}{3}
\]
This equation shows the relationship between the number \( x \) and the zip \( z \). If you have a specific value for \( x \), you can substitute it into this equation to find \( z \).
Answer
3 times the difference of a number and 10 equals the sum of 25 and that same number
Answered by
GPT-4o mini
Let's denote the unknown number as \( x \). According to your statement, we can set up the following equation:
\[
3(x - 10) = 25 + x
\]
Now, let's solve this equation step by step.
1. Distribute the 3 on the left side:
\[
3x - 30 = 25 + x
\]
2. Next, isolate \( x \) on one side. Start by subtracting \( x \) from both sides:
\[
3x - x - 30 = 25
\]
This simplifies to:
\[
2x - 30 = 25
\]
3. Now, add 30 to both sides to isolate the term with \( x \):
\[
2x = 25 + 30
\]
\[
2x = 55
\]
4. Finally, divide both sides by 2 to solve for \( x \):
\[
x = \frac{55}{2}
\]
\[
x = 27.5
\]
Thus, the number is \( x = 27.5 \).
\[
3(x - 10) = 25 + x
\]
Now, let's solve this equation step by step.
1. Distribute the 3 on the left side:
\[
3x - 30 = 25 + x
\]
2. Next, isolate \( x \) on one side. Start by subtracting \( x \) from both sides:
\[
3x - x - 30 = 25
\]
This simplifies to:
\[
2x - 30 = 25
\]
3. Now, add 30 to both sides to isolate the term with \( x \):
\[
2x = 25 + 30
\]
\[
2x = 55
\]
4. Finally, divide both sides by 2 to solve for \( x \):
\[
x = \frac{55}{2}
\]
\[
x = 27.5
\]
Thus, the number is \( x = 27.5 \).