## When a player in a certain game tossed…

## Solution:

We are given that when a coin was tossed a certain number of times, 4 more heads than tails resulted. If we let H = the number of times heads is tossed and T = the number of times tails is tossed, we can create the following equation:

H = T + 4

We need to determine the value of H.

**Statement One Alone: **

The player tossed the coin 24 times.

Using the information in statement one we can create the following equation:

T + H = 24

Since H = T + 4, we can substitute T + 4 for H in the equation T + H = 24.

T + T + 4 = 24

2T = 20

T = 10

Since T = 10, H = 10 + 4 = 14.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

Using the information in statement two we can create the following equation:

3H + T = 52

Since H = T + 4, we can substitute T + 4 for H in the equation 3H + T = 52.

3(T + 4) + T = 52

3T + 12 + T = 52

4T = 40

T = 10

Since T = 10, H = 10 + 4 = 14.

Statement two alone is also sufficient to answer the question.

**Answer:** D