The total number of people in a survey is T. The number of males in the survey is x and the number of doctors is y. The number of doctors that are male is z. Write algebraic expressions for the following using any of the variables x, y, z and T.
a. The number who are neither male nor a doctor
b. The number who are male but not a doctor
c The number who are female or a doctor
Please explain how you got the answer. Thank you
To write algebraic expressions for the given scenarios, we can use set operations and the given variables x, y, z, and T.
a. The number who are neither male nor a doctor:
To find the number of people who are neither male nor a doctor, we need to subtract the number of males from the total number of people in the survey and then subtract the number of doctors from that result.
The expression can be written as:
T - x - y
Explanation: We start with the total number of people in the survey (T). From that, we subtract the number of males (x) to get the number of females. Then, we further subtract the number of doctors (y) to exclude those who are doctors. The resulting expression gives us the number of people who are neither male nor a doctor.
b. The number who are male but not a doctor:
To find the number of people who are male but not a doctor, we need to subtract the number of doctors that are male (z) from the total number of males (x).
The expression can be written as:
x - z
Explanation: We start with the total number of males (x). From that, we subtract the number of doctors that are male (z). The resulting expression gives us the number of males who are not doctors.
c. The number who are female or a doctor:
To find the number of people who are either female or a doctor, we need to add the number of females (T - x) to the number of doctors (y).
The expression can be written as:
(T - x) + y
Explanation: We start with the total number of people in the survey (T). From that, we subtract the number of males (x) to get the number of females. Then, we add the number of doctors (y). The resulting expression gives us the number of people who are either female or a doctor.