Final answer:
The maximum number of consecutive trades that the stockbroker can lose before his profitable trades drop below 50 is 30.
Step-by-step explanation:
To find the maximum number of consecutive trades that the stockbroker can lose before his profitable trades drop below 50, we need to calculate the number of profitable trades and then subtract it from 80. Since the stockbroker currently has a profit of 80, we know that he has made 80 profitable trades.
Let's assume that the stockbroker loses x consecutive trades. Each losing trade will decrease his profit by 1. So, the total decrease in profit will be x. The difference between his initial profit of 80 and a decrease of x should be greater than or equal to 50. Therefore, the inequality equation we can set up is:
80 - x ≥ 50
By solving this inequality, we can calculate the maximum number of consecutive trades that the stockbroker can lose before his profitable trades drop below 50.
Subtracting 80 from both sides:
-x ≥ 50 - 80
-x ≥ -30
Multiplying both sides by -1 (which reverses the inequality sign):
x ≤ 30
Therefore, the maximum number of consecutive trades that the stockbroker can lose before his profitable trades drop below 50 is 30 trades.