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Matt gets \$1000 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?

I feel this question is missing some information but the book has a solution. Am i missing something?

user1772052
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3 Answers3

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long time has passed since the question was asked but i'll explain it for newest guests.

So, if we take "n" as the # of sales (n=# of sales) and "T" for total comissions; then our first equaiton is; 250n=T, then, for instance, Matt gets a big sale and his total comissions rise to T+1000 and number of sales rise to "n+1" and new average commission becomes 400$. Therefore we have two equations.

250n=T

400(n+1)=1000+T

on first equation, if we multiply each side by minus "-", equation won't change. then;

-250n=-T

400n+400=1000+T our new equations. Then we could sum each side of equations.

So,

150n=600, then n=4

our final amount of sales is (n+1), then the number of sales that Matt has made is n+1 = 4+1 = 5

answer is 5

Gökhan E.
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Hint: Let $n$ be the number of sales Matt has made, $T$ the total commission Matt has earned, including the most recent sale. How would you calculate his current average commission (if you didn't know it already) from these values? How would you calculate the average commission prior to his most recent sale? From these calculations, you will have two linear equations in the two variables $n$ and $T$, from which you should be able to determine $n$ (and $T$, of course).

Cameron Buie
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  • So for instance can i set up equation as follows? n = # of sales.T = total commission.

    old : 250n = T new : 400n = T + 1000

    is my setup correct?

     – user1772052 Sep 16 '13 at 15:53
  • Very close, but not quite. Indeed, if you were to solve that system, you'd find that Matt had made a non-whole number of sales, which doesn't make sense. If his current total commission is $T$ and he has made $n$ sales, then his current average commission is $T/n,$ yes? Well, his current average commission is $400$, so that gives us the equation $$400n=T.$$ Now, before he made his most recent sale, how many sales had he made? What was his total commission before he made his most recent sale? Can you build the second equation from the answers to these questions? – Cameron Buie Sep 16 '13 at 17:27
  • 250(n-1) = T -1000

    I believe this would be the equation for sales before the big sale.

     – user1772052 Sep 16 '13 at 18:45
  • Exactly right! Can you take it from there? – Cameron Buie Sep 16 '13 at 18:56
  • yup i did. thank you for teaching me rather then suggesting a quick solution. appreciate it. – user1772052 Sep 16 '13 at 20:51
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You can even do it by trial and error. Since his average commission is raised 150 dollars. Then we know his original average was 250.By trial and error I multiplied 250*4=1000 Add another 1000 dollars and we get 2000. And 2000/5 is 400 average. Thus he has made 5 sales.

user60887
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