Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?
OA: 5
please EXPLAIN how to handle such commission problems![/u]
average problem 1
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When looking at these problems I find it easiest to set up an simple formula for "old" and "new", keeping in mind the formula averages: Average = Sum / N , where N = number of elements.
In this example, we are given the new average (400) and told that it is 150 greater than the old average, so the old average is 400-150= 250.
So now, we have these to plug in:
Old Average ===> 250 = (Old Sum) / N
New Average: ===> 400 = (New Sum)/ N + 1
The "+1" is to account for the additional sale.
We are then told that the 1,000 is the additional value of the additional "sale". We incorporate this information into the "new average....
So , for new average, our new formula is:
400 = (Old Sum + 1000) / N + 1
From our original equation, we can now plug in "Old Sum"!
250 = Old Sum / N ===> Old Sum = 250n
Plug it in to get:
400 = 250n +1000 / N +1
Now we can solve for N, Which is 4, but dont forget to add 1 to get total sales of 5.
In this example, we are given the new average (400) and told that it is 150 greater than the old average, so the old average is 400-150= 250.
So now, we have these to plug in:
Old Average ===> 250 = (Old Sum) / N
New Average: ===> 400 = (New Sum)/ N + 1
The "+1" is to account for the additional sale.
We are then told that the 1,000 is the additional value of the additional "sale". We incorporate this information into the "new average....
So , for new average, our new formula is:
400 = (Old Sum + 1000) / N + 1
From our original equation, we can now plug in "Old Sum"!
250 = Old Sum / N ===> Old Sum = 250n
Plug it in to get:
400 = 250n +1000 / N +1
Now we can solve for N, Which is 4, but dont forget to add 1 to get total sales of 5.
- Gurpinder
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thanks rochellemissrochelle wrote:When looking at these problems I find it easiest to set up an simple formula for "old" and "new", keeping in mind the formula averages: Average = Sum / N , where N = number of elements.
In this example, we are given the new average (400) and told that it is 150 greater than the old average, so the old average is 400-150= 250.
So now, we have these to plug in:
Old Average ===> 250 = (Old Sum) / N
New Average: ===> 400 = (New Sum)/ N + 1
The "+1" is to account for the additional sale.
We are then told that the 1,000 is the additional value of the additional "sale". We incorporate this information into the "new average....
So , for new average, our new formula is:
400 = (Old Sum + 1000) / N + 1
From our original equation, we can now plug in "Old Sum"!
250 = Old Sum / N ===> Old Sum = 250n
Plug it in to get:
400 = 250n +1000 / N +1
Now we can solve for N, Which is 4, but dont forget to add 1 to get total sales of 5.