Question

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. $45$

Answer 1

Answer: (B)

$36$

Out of the $35$ parents who agreed to supervise children during the school picnic, $11$ parents are also bringing refreshments, so $35-11=24$ parents are only supervising children. Let $x$ be the number of parents who volunteered to bring refreshments, and let $y$ be the number of parents who declined to supervise or to bring refreshments. The fact that the number of parents who volunteered to bring refreshments is $1.5$ times the number who did not volunteer at all can then be expressed as $x=1.5y$. A Venn diagram, such as the one below, can be helpful in answering problems of this kind.

Then,the sum of the sections can be set equal to the total number of parents at the picnic, and the equation can be solved for $y$:

$y+24+x=84$ sum of sections $=$ total parents at picnic

$y+x=60$ subtract $24$ from each side

$y=60-x$ subtract $x$ from each side

Then, substituting the value $60-x$ for $y$ in the equation $x=1.5y$ gives the following:

$x=1.5(60-x)$

$x=90-1.5x$ distribute the $1.5$

$2.5x=90$ add $1.5x$ to both sides

$x=36$ divide both sides by $2.5$

The correct answer is B.