need your assistance to solve amusement park problem

[defeated_soldier]

85 children went to an amusement park , where they could ride on the merry-go-round , roller coaster , and wheel . It was known that 20 of them took all the three rides , and 55 of them took at least two of the three rides . Each ride cost Re 1 , and the total receipt of the amusement park from these children was Rs . 145

(1) How many children did not try any of the rides ?
(a)5
(b)10
(c)15
(d)20

(2) How many children took exactly one ride ?
(a)5
(b)10
(3)15
(d)20



My effort :

In order to solve this problem , i remember the set theorem

n(AUBUC) = n(A)+n(B)+n(C) -n(A Intersection C) - n(A Intersection B) - n (B Intersection C)+n(A Intersection B Intersection C)


if i map this into the problem , i get

n(AUBUC) = 85
n(A Intersection B Intersection C) = 20

however , i cant put 55 into the above equation .


I am really stuck here to solve this problem and need your assistance .

can you help me to figure out this problem

Thank you






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[arthur ohlsten]

rides.................# children..................cost
3..........................20...........................60
2...........................35..........................70
1............................15..........................15
0...........................15............................0
_________________________________________
totals 85 145

1) answer C
2) answer C

Arthur

 

[defeated_soldier]

rides.................# children..................cost
3..........................20...........................60
2...........................35..........................70
1............................15..........................15
0...........................15............................0
_________________________________________
totals 85 145

1) answer C
2) answer C

Arthur

could you please tell , how did you get 1 ride=15 children and 0 ride = 15 children ?

please explain

thank you

 

[arthur ohlsten]

we know 20 children went on 3 rides and spent 60
we know 35 children went on 2 rides and spent 70

so we know 55 children went on 2 or 3 rides and spent 130
we must spend 15 more so 15 children went on 1 ride and spent 15

we know [55+15] 70 children went on rides and spent [130+15]145
the remaining 15 children went on no rides
Arthur