Let the unknown number be represented by x. According to the problem, when we take two thirds of this number and subtract 9 from it, we should get a result of 7. We can express this relationship with the following equation:
\( \frac{2}{3}x – 9 = 7 \)
To solve for x, we first add 9 to both sides of the equation:
\( \frac{2}{3}x = 7 + 9 \)
This simplifies to:
\( \frac{2}{3}x = 16 \)
Next, we can eliminate the fraction by multiplying both sides of the equation by 3:
\( 2x = 16 \times 3 \)
This gives us:
\( 2x = 48 \)
Now we divide both sides by 2 to solve for x:
\( x = \frac{48}{2} \)
This results in:
\( x = 24 \)
Thus, the number we are looking for is 24.