Question

Peter says, if you subtract 11 from my number and multiply the difference by -4, the result is -108. What is Peter's number?

Answer 1

To find Peter's number, we set up and solved the equation (x - 11) * -4 = -108, where x represents Peter's number. By simplifying the equation, we discovered that Peter's number is 38.

Step-by-step explanation:

The student is tasked with solving an equation based on Peter's statement that involves simple arithmetic and algebraic manipulation. To solve this, we need to construct an equation based on the given information and perform a series of mathematical operations to find Peter's number. The equation starts with Peter's number, subtracts 11 from it, multiplies the result by -4, and equates it to -108.

Step-by-step Solution

1. Let's denote Peter's number as x. According to Peter, subtracting 11 from his number is expressed as x - 11.
2. Multiplying the difference by -4 gives us (x - 11) * -4. Peter says the result of this operation is -108.
3. Setting up the equation: (x - 11) * -4 = -108.
4. Divide both sides of the equation by -4 to isolate the term with x: x - 11 = -108 / -4.
5. Simplify the right side: x - 11 = 27.
6. Add 11 to both sides to solve for x: x = 27 + 11.
7. Finally, we find that Peter's number is 38.

Hence, the answer to the question is that Peter's number is 38.