Bunuel wrote:

Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the company’s average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A?

A. 25%

B. 30%

C. 37.5%

D. 56.25%

E. 75%

Kudos for a correct solution.

800score Official Solution:This is a tricky weighted average problem. If there are only two price levels, $75 and $175, and the average customer pays $100, then the number of customers who pay $75 must be 3 times the number of customers who pay $175, since $100 is 3 times as close to $75 as it is to $175.

We can show this algebraically:

If there are A customers with plan A, and B customers with plan B, then the total revenue is $75A + $175B.

Since the average customer pays $100, we know that

$100 = ($75A + $175B) / (A + B)

$100(A + B) = ($75A + $175B)

$100A + $100B = $75A + $175B

$25A = $75B

A = 3B.

Since there are 3 times as many $75 clients as $175 clients, for every $175 received from Plan B customers, 3($75) = $225 is received from Plan A customers, and the percent of revenue from customers with Plan A is:

$225/($225 + $175) = $225/$400 = 56.25%.

The correct answer is choice (D).