Question 1201030: 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 340 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 400. What percentage of
respondents answered "yes," "no," and "not sure"? (Let x represent the number of
respondents who answered "yes", y represent the number of respondents who
answered "no", and z represent the number of respondents who answered "not
sure".)
? = 1000
? = 340
? = 400
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website! ...1000 adults...(yes's) + (no's) + (not sure's) = 1000
x + y + z = 1000 ...340 answered "no" or "not sure."...(no's) + (not sure's) = 340
y + z = 340 ...the number of those who answered "yes"
exceeded the number of those who answered
"no" by 400...(yes's) - (no's) = 400
x - y = 400
Edwin
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Building from what the tutor Edwin McCravy mentioned
x + y+z = 1000
x + y+z = 1000
x + 340 = 1000
This replacement, aka substitution, is valid because y+z = 340 was the second equation he formed.
Solving for x:
x+340 = 1000
x = 1000-340
x = 660
There were 660 people who responded "yes" (they find online travel reviews trustworthy).
We can then plug this into the third equation he formed to find y.
x-y = 400
660-y = 400
-y = 400-660
-y = -260
y = 260
There were 260 people who responded "no" (they don't find online travel reviews trustworthy).
Use that value of y to determine z.
y+z = 340
260+z = 340
z = 340-260
z = 80
There were 80 people who weren't sure if the online travel reviews were trustworthy or not.
Check:
x+y+z = 1000
660+260+80 = 1000
1000 = 1000 ..... 1st equation works
and
y+z = 340
260+80 = 340
340 = 340 ....... 2nd equation works
and
x-y = 400
660-260 = 400
400 = 400 ...... 3rd equation works
All three original equations are true for (x,y,z) = (660,260,80)
Those values are fully confirmed.
Now to compute percentages, we divide each by 1000
x = 660 leads to x/1000 = 660/1000 = 0.66 = 66%
Therefore, 66% of the participants said "yes".
y = 260 leads to y/1000 = 260/1000 = 0.26 = 26%
26% of the participants said "no".
z = 80 leads to z/1000 = 80/1000 = 0.08 = 8%
8% of the participants said "not sure".
Summary:
x = 660 ----> 66% said "yes"
y = 260 ----> 26% said "no"
z = 80 -----> 8% said "not sure"
Note the percentages add to 100 percent ( 66+26+8 = 100)
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