Question

Write the equation that satisfies the parameters: two times the sum of a number and 24 equals the difference of 76 and that same number.

Answer 1

Let's denote the unknown number as \( x \).

According to the problem, we need to translate the statement into an equation. The statement says:

"Two times the sum of a number and 24" can be written as:
\[
2(x + 24)
\]

The phrase "equals the difference of 76 and that same number" can be expressed as:
\[
76 - x
\]

Putting it all together, we set up the equation:
\[
2(x + 24) = 76 - x
\]

Now, we can simplify and solve the equation.

Expanding the left side:
\[
2x + 48 = 76 - x
\]

Next, we add \( x \) to both sides to get all \( x \) terms on one side:
\[
2x + x + 48 = 76
\]
\[
3x + 48 = 76
\]

Now, subtract 48 from both sides:
\[
3x = 76 - 48
\]
\[
3x = 28
\]

Finally, divide by 3:
\[
x = \frac{28}{3}
\]

Thus, the equation that satisfies the parameters is:
\[
2(x + 24) = 76 - x
\]