Multiple choice

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?

  1. $6$
  2. $5$
  3. $4$
  4. $7$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of sales. (Total + 1000) / (n+1) = 400. Total = 400n. 400n + 1000 = 400(n+1) + 150(n+1) is wrong. Correct: Previous average = 400 - 150 = 250. 250n + 1000 = 400(n+1). 250n + 1000 = 400n + 400. 600 = 150n. n = 4. The new total is 5 sales (4 original + 1 new).

AI explanation

Let the original number of sales be n. Matt's new average commission is 400, and his old average was 400 minus 150 = 250. The total commission from the old sales was 250n, and adding the new sale gives the equation (250n + 1000) / (n + 1) = 400. Solving this yields 250n + 1000 = 400n + 400, which simplifies to 150n = 600, so n = 4. Including the big sale, the total number of sales he has made is 4 + 1 = 5.

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