valerie tells robbie "im thinking of a number between 1 and 50. if i divide the number by 4, then add 5, then subtract 6 i get 6."

Answer 1

To solve for the number Valerie is thinking of, let's follow the operations she described step-by-step with a variable representing the unknown number.

Let the number be \( x \).

According to Valerie:

1. Divide the number by 4: \( \frac{x}{4} \)
2. Add 5: \( \frac{x}{4} + 5 \)
3. Subtract 6: \( \left(\frac{x}{4} + 5\right) - 6 = 6 \)

Now we can set up the equation:

\[ \frac{x}{4} + 5 - 6 = 6 \]

This simplifies to:

\[ \frac{x}{4} - 1 = 6 \]

Now we will isolate \( \frac{x}{4} \):

\[ \frac{x}{4} = 6 + 1 \] \[ \frac{x}{4} = 7 \]

Next, we solve for \( x \) by multiplying both sides by 4:

\[ x = 7 \times 4 \] \[ x = 28 \]

So, the number Valerie is thinking of is 28.