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

Hint:

In set problems, break down the total into smaller groups and use variables to represent the unknowns.

Answer 1

The Correct Option is D

Step 1: Set up the relationships.
Let \( x \) be the number of parents who neither volunteered to supervise children nor volunteered to bring refreshments. Then the number of parents who volunteered to bring refreshments is \( 1.5x \).
Step 2: Write the total number of parents.
The total number of parents is 84, which can be broken down as: \[ 35 \text{ (supervised)} + 11 \text{ (both supervised and refreshments)} + x + 1.5x = 84 \] Simplify: \[ 35 + 11 + 2.5x = 84 \quad \implies \quad 46 + 2.5x = 84 \quad \implies \quad 2.5x = 38 \quad \implies \quad x = 15.2 \] Thus, the number of parents who volunteered for refreshments is: \[ 1.5 \times 15.2 = 42 \] \[ \boxed{42} \]