We are given a system of equations where x represents the number of servers and y represents the number of bus persons.
25 x+8 y=249 & (I) x+ y=12 & (II)
To determine which of the given options is true, we will solve this system.
Solving the System
Let's use the Substitution Method. The Substitution Method is usually a good choice when one of the variables is already isolated or has a coefficient of 1. First we will isolate the y-variable in Equation (II).
25x+8y=249 x+y=12
⇔
25x+8y=249 y=12-x
Next we will substitute 12-x for y in Equation (I) and solve it for x.
We have that on the given night the company employs 9 servers and 3 bus persons.
Determining the Correct Option
Let's go through the statements one by one and determine if they are correct or not.
F: Fewer than 2 bus persons were working. There were 3 bus persons working that day, which is more than 2. The statement is incorrect.
G: More than ten servers were working. We have found that the number of servers working were 9, which is fewer than 10. The statement is incorrect.
H: 50 % of the people working were bus persons. Of the 12 people working, only 3 were bus persons, which is less than half. This statement is also incorrect.
I: 75 % of the people working were servers. Let's determine if this statement is correct or not.
Recall the percent proportion.
a/b=p/100
The total b were the total number of people working that night 12. The part a were the number of servers which was 9. Let's find the percent p.
