SOLUTION: Hi, Please help me to solve step-by-step on these questions. Thank you very much. 1. Define your variables and set up a system of two equations and two unknowns for the fol

Algebra ->  Linear-equations -> SOLUTION: Hi, Please help me to solve step-by-step on these questions. Thank you very much. 1. Define your variables and set up a system of two equations and two unknowns for the fol      Log On


   

Question 1112187: Hi,
Please help me to solve step-by-step on these questions.
Thank you very much.
1. Define your variables and set up a system of two equations and two unknowns for the following problem, then solve the system and answer the question. Show all your work!
Excedrin surveyed workers in various professions who get headaches at least once a year on the job. Nine more accountants than waiters/waitresses in the survey got a headache. If the combined number of accountant and waiters/waitresses that got a headache was 163, how many people in each of those professions got a headache? What method did you use to solve this problem?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let  A  be the number of accountants and
let  W  be the number of waiters/waitresses.


The problem says

A - W =   9,     (1)
A + W = 163.     (2)
------------------------------ Add the two equations.

                               In this way you eliminate W:

2A = 9 + 163 = 172  ====>  A = 172%2F2 = 86.


Then from eq(2)  W = 163-A = 163 - 86 = 77.


Answer.  86 accountants  and  77 waiters/waitresses.


Check.   Check it on your own - it is VERY USEFUL exercise for you, which will help you better to understand the problem.

P.S.   I used the Elimination method solving the system of equations.