Skip navigation.
Home
...where Math lovers and haters meet!

The annual sophomore class picnic is a plan by committee consisting of 17 members.

The annual sophomore class picnic is a plan by committee consisting of 17 members. A vote to determine whether the picnic should be held at the beach or in the mountains resulted in a victory for the beach location. However if the two committee members had changed the vote from favoring the beach to favoring the mountains, the mountain site would have won by one vote. How many votes did each picnic location receive?

Solution:

Based on the problem data, let us use the following variable representation:

            x = beach voter
           y = mountain voter

 
x + y    = 17                 [Eq. 1]
x – 2 = y + 1                [Eq. 2]
 
Solving the two equations in two unknowns give:
 
x + y                = 17                 [Eq. 1]
xy                = 1 + 2             [Eq. 2]
2x                    = 20
x                      = 10
 
We can solve for y using Eq. 1:
 
x + y    = 17
10 +
y = 17
y          = 17 – 10
y          = 7
 
Therefore, there 10 who voted for a beach picnic and 7 voted for mountain picnic.
 
Check:
x + y    = 17                 [Eq. 1]
10 + 7 = 17
17        = 17
 
If 2 beach voters voted for mountain picnic:
 
x – 2    = ?
10 – 2 = 8
 
The mountain picnic would have won by 1 vote:
 
y + 2    = ?
7 + 2    = 9