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.
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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).
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This question can be easily solved by using allegation.
the ratio of plan A to plan B will be
(175-100)/(100-75) =75/25 = 3/1

for every 3 plan A there is 1 plan B
so company earns 225 from 3 plan A and 175 from 1 plan B.
total 400
revenue percent from plan A will be
(225/400)*100 = 56.25 %

Answer:- D

Hi All,

All Average Formula questions can be solved with that formula (just plug the numbers and variables into the formula). This question asks you to do MORE than just use the average formula though….

A = Number of customers for Plan A
B = Number of customers for Plan B

[75A + 175B] / [A + B] = 100

Now there's just a few algebra steps:

75A + 175B = 100A + 100B

75B = 25A

3B = A

This tells us that the number of people who bought Plan A is THREE TIMES the number of people who bought Plan B.

If B=1 and A=3 then the revenue would be:

1(175) + 3(75)

175 + 225 = 400 total dollars

The question asks "what percentage of revenue comes from Plan A"

225/400 = 9/16 = 56.25%

Final Answer:

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