Question

Juwan is thinking of a number. Twice the sum of Juwan’s number and 12 is equal to four less than three times Juwan’s number. What number is Juwan thinking of

Answer 1

Let Juwan's number be represented by \( x \). The problem states that twice the sum of Juwan's number and 12 is equal to four less than three times Juwan's number. We can translate this statement into an equation:

\[
2(x + 12) = 3x - 4
\]

Now, let's simplify the equation step-by-step.

1. Expand the left side:

\[
2x + 24 = 3x - 4
\]

2. Next, move the \( 2x \) term to the right side by subtracting \( 2x \) from both sides:

\[
24 = 3x - 2x - 4
\]

This simplifies to:

\[
24 = x - 4
\]

3. Now, add 4 to both sides to isolate \( x \):

\[
24 + 4 = x
\]

\[
x = 28
\]

Thus, Juwan is thinking of the number \( \boxed{28} \).

To verify, we can substitute \( x = 28 \) back into the original condition:

- Calculate twice the sum of \( 28 \) and \( 12 \):

\[
2(28 + 12) = 2 \times 40 = 80
\]

- Calculate four less than three times \( 28 \):

\[
3 \times 28 - 4 = 84 - 4 = 80
\]

Since both sides are equal (80 = 80), the solution is confirmed. Juwan's number is indeed \( \boxed{28} \).