If p * q = 2p + pq + q, find p when ( p * 2) - (p * 1) = 40

Answer Details

To solve the given problem, we first need to understand the operation defined by p * q. According to the definition, p * q = 2p + pq + q. We need to find the value of p that satisfies the equation (p * 2) - (p * 1) = 40.

Let's break down the operations step by step:

• First, find p * 2:

  p * 2 = 2p + p(2) + 2

  Simplifying this, we get: p * 2 = 2p + 2p + 2 = 4p + 2

• Next, find p * 1:

  p * 1 = 2p + p(1) + 1

  Simplifying this, we get: p * 1 = 2p + p + 1 = 3p + 1

Using these simplifications, we substitute into the equation: (p * 2) - (p * 1) = 40

Substitute the expressions we found:

(4p + 2) - (3p + 1) = 40

Now, simplify the equation:

4p + 2 - 3p - 1 = 40

This simplifies to: 4p - 3p + 2 - 1 = 40

Further simplifying gives: p + 1 = 40

Subtract 1 from both sides to solve for p:

p = 40 - 1

p = 39

Therefore, the value of p is 39.