Question

Write the equation that satisfies the parameters two times the sum of a number and twenty four equals the difference of seventy six and that same number

Answer 1

Let the unknown number be represented by \( x \). According to the problem, we can set up the equation in the following way:

The sum of the number and twenty-four is \( x + 24 \). Two times this sum is \( 2(x + 24) \).

The difference of seventy-six and the same number is \( 76 - x \).

We can equate the two expressions:

\[
2(x + 24) = 76 - x
\]

Now, you can simplify and solve this equation.

1. Distribute on the left side:
\[
2x + 48 = 76 - x
\]

2. Add \( x \) to both sides:
\[
2x + x + 48 = 76
\]
\[
3x + 48 = 76
\]

3. Subtract 48 from both sides:
\[
3x = 76 - 48
\]
\[
3x = 28
\]

4. Divide by 3:
\[
x = \frac{28}{3}
\]

So the solution to the equation you set up is \( x = \frac{28}{3} \).