Group: how many parents volunteered to bring food?

[Jackie9988]

Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments, how many of the parents volunteered to bring refreshments?

A) 25 B) 36 C) 38 D) 42 E) 45

Out of the 35 parents who agreed to supervise children, 11 parents are also bringing refreshments, so 35-11 = 24 parents are only supervising children.
X = # of parents who volunteered to bring refreshments
Y = # of parents who declined to supervise OR bring refreshments
Parents bringing refreshments = 1.5 • parents doing nothing: X = 1.5Y
Venn diagram can help answer this.

Y + 24 + X = 84
Y + X = 60
Y = 60 – X
Substitute the value 60 – X for Y in the equation X = 1.5Y
X = 1.5 (60 – X)
X = 90 – 1.5X
2.5X = 90
X = 36
Answer: B

HOW MANY PARENTS ARE DOING NEITHER (SUPERVISOR OR BRING REFRESHMENTS? (Please excuse "all caps" - I cannot use bold or underline.) I think 24 parents are doing neither, but I am not sure.

 

[Deleted member 4993]

Re: Group

You are correct.

You should do this problem by Venn diagram. Anyway, algebraically (and diagramatically) there are four sections.

Parents who do supervise and do bring food = x

Parents who do supervise and do not bring food = y

Parents who do not supervise and do bring food = w

Parents who do not supervise and do not bring food = z

Given

x + y = 35

x = 11 --> y = 24

x + w = 1.5*z

You need to find

(x + w) = ??
Now continue...