SOLUTION: Formulate a system of equations for the situation below and solve. In a survey of 1000 adults aged 18 and older, the following question was posed: "Are other travelers' online

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Formulate a system of equations for the situation below and solve. In a survey of 1000 adults aged 18 and older, the following question was posed: "Are other travelers' online       Log On


   

Question 1107280: Formulate a system of equations for the situation below and solve.
In a survey of 1000 adults aged 18 and older, the following question was posed: "Are other travelers' online reviews trustworthy?" The participants were asked to answer "yes," "no," or "not sure." The survey revealed that 310 answered "no" or "not sure." It also showed that the number of those who answered "yes" exceeded the number of those who answered "no" by 420. What percentage of respondents answered "yes," "no," and "not sure"?
(a) "yes"
%
(b) "no"
%
(c) "not sure"
%
Answer by ikleyn(52901) About Me  (Show Source):
You can put this solution on YOUR website!
.
You are given 
    1000 adults, in all.                  (1)

    310 answered "no" or "not sure".      (2)

    Those who answered "yes" exceeded the number of those who answered "no" by 420.     (3)


Solution 

It follows from statements (1) and (2) that the number of those who said "YES" is 

    1000 - 310  =  690.     (4)



Then from the statement (3), the number of those who said "NO" is

     690 - 420 = 270.



Finally, the number of those who said "NOT SURE"  is

    1000 - (690 + 270) = 40.



Having these numbers, you can easily complete all necessary calculations on your own.


Lesson to learn from this solution: 

     1.  The formulation of the problem contains a lot of "white noise" which only distract your attention (and is specially designed to distract it !)

         Therefore, when solve such problems, try eliminate this "noise" as much as you can.

         To do it, I specially reformulated the condition at the very beginning of my post by throwing away everything that does not matter.

         This step is "reducing".


     2.  After "reducing" is completed, look on the rest and think.


     3.  It is the key.