Problem Solving

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]

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.

C=1000

Average=Sum of C/n

250=Sum/n

Sum=250n

400=Sum+1000/n+1


400=250n+1000/n+1

400n+400=250n+1000

150n=600

n=4

n+1=5

missrochelle 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.

thanks rochelle