Question
Fourteen times a number is the same as 24 more than 6 times the number. Find the number.
Answers
GPT-4o mini
Let the unknown number be represented by \( x \). According to the problem, we have the equation:
\[
14x = 6x + 24
\]
To solve for \( x \), we first isolate \( x \) on one side of the equation. We can do this by subtracting \( 6x \) from both sides:
\[
14x - 6x = 24
\]
This simplifies to:
\[
8x = 24
\]
Next, we divide both sides by 8 to solve for \( x \):
\[
x = \frac{24}{8} = 3
\]
Thus, the number is
\[
\boxed{3}
\]
To confirm our solution, we check the original equation by substituting \( x = 3 \):
Calculating the left side:
\[
14 \times 3 = 42
\]
Calculating the right side:
\[
6 \times 3 + 24 = 18 + 24 = 42
\]
Both sides are equal, as \( 42 = 42 \), confirming that our solution is correct. Therefore, the number is indeed
\[
\boxed{3}
\]
\[
14x = 6x + 24
\]
To solve for \( x \), we first isolate \( x \) on one side of the equation. We can do this by subtracting \( 6x \) from both sides:
\[
14x - 6x = 24
\]
This simplifies to:
\[
8x = 24
\]
Next, we divide both sides by 8 to solve for \( x \):
\[
x = \frac{24}{8} = 3
\]
Thus, the number is
\[
\boxed{3}
\]
To confirm our solution, we check the original equation by substituting \( x = 3 \):
Calculating the left side:
\[
14 \times 3 = 42
\]
Calculating the right side:
\[
6 \times 3 + 24 = 18 + 24 = 42
\]
Both sides are equal, as \( 42 = 42 \), confirming that our solution is correct. Therefore, the number is indeed
\[
\boxed{3}
\]