## At a certain picnic…

## Solution:

We are given that at a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. Let’s define two variables describing the number of scoops of ice cream for the picnic guests.

s = number of guests who received a single scoop of ice cream

d = number of guests who received a double scoop of ice cream

We need to determine how many of the guests were served a double scoop; that is, we need to determine the value of variable d.

**Statement One Alone: **

At the picnic, 60% of the guests were served a double scoop of ice cream.

Since we only know the percentage of the guests who were served a double scoop of ice cream and we do not know the total number of guests, we cannot determine the number of guests who were served a double scoop of ice cream, and thus we cannot determine a value for d. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

A total of 120 scoops of ice cream were served to all the guests at the picnic.

Since we know that 120 scoops of ice cream were served to all the guests at the picnic, and each single scoop has 1 scoop and each double scoop has 2 scoops, we can create the following equation:

s + 2d = 120

We cannot determine a value for d. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

Let t = total number of guests. From statement one, d =0.6t. Furthermore, s =0.4t. From statement two, we know s + 2d = 120. Rewriting the equation in terms of t, we have:

0.4t + 2(0.6t) = 120

0.4t + 1.2t = 120

1.6t = 120

t = 75

Since t = 75, d = 0.6 x 75 = 45. Thus, there were 75 guests, and 45 of them were served a double scoop of ice cream.

**Answer:** C