Of 600 households surveyed, 200 spent at least $80 per month on both

Question

Of 600 households surveyed, 200 spent at least $80 per month on both cola and juices, 100 spent at least $80 per month on cola but not juices, and for every household that did not spend at least $80 per month on cola or juices, 4 spent at least $80 per month on juices but not cola. How many of the households surveyed spent at least $80 per month on juices but not cola?

A. 60
B. 75
C. 240
D. 300
E. 440

A. 60
B. 75
C. 240
D. 300
E. 440

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dp1234 · Answer

If you ignore the at least $80 a month, the question becomes straightforward. 
Total, T = 600
only cola, c=100
both cola and juice, b=200
let only juice be j and neither cola or juice be n. Its given j=4n or n=j/4.
T = c +j + b + n
600 = 100 + j + 200 + j/4
300 = 5j/4 -> j= 240.

C.

laborumplaceat · Answer

The problem is best solved by breaking the 600 households into four mutually exclusive regions using a Venn Diagram:

Only Cola:  100 
  Both Cola & Juice:  200 
  None (neither Cola nor Juice):  Let this be x 
  Only Juice:  Given the 1:4 ratio relative to "None," this is 4x

Final Answer: 
The number of households that spent on  Juice only  is 4x = 4(60) = 240.

vasu1104 · Answer

total = 600
spending on both cola and juices = 200
spending on only cola = 100

say number of people spending on neither of things - x
as per stem, for every X there are 4 people spending on only juices. so spending on only juices = 4X

find people spending on only juices= ?

we know people in both category are= 200
and we also know people in only cola = 100
so people in overall cola = 300
so based on that people in not in cola = 300 (600-300)
only on juices = 4x
neither on both = x

so 4x + x = 300
x= 60

so people spending on only juice = 240

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=gU6VIu8dEfA

Of 600 households surveyed, 200 spent at least $80 per month on both

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Of 600 households surveyed, 200 spent at least $80 per month on both

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