M06-36

The '6' in the denominator acts as a constant factor in the original equation \(\frac{MT}{6}=W\). It remains the same, regardless of any changes in the individual commissions of Mike, Tom, and Walt. Since it serves as a scaling factor, it does not impact the relationship between the agents' commissions.

When calculating the new product of their commissions for the current month, there is no need to account for the '6' in the denominator. It remains a constant factor and does not affect the calculation. We only need to focus on the changes in Mike's and Tom's individual commissions and how these changes influence the overall product of the three commissions.

If you try plugging numbers into the equation, you will see how the '6' in the denominator does not impact the relationship between the agents' commissions. Let's assume the following values for M, T, and W in the last month. Using M = 30, T = 10, and W = 50, the original equation holds true. After adjusting the commissions:

Mike's commission: 1.6M = 48
Tom's commission: 0.5T = 5

The product of their commissions (240) decreased by 20%. To maintain the relationship, we decrease Walt's commission by 20%:

New W = 0.8(50) = 40

The updated equation holds true: \(\frac{(48)(5)}{6} = 40\).

Hope it's clear.