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# When a player in a certain game tossed a coin a number of

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Re: When a player in a certain game tossed a coin a number of [#permalink]
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When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin. How many times did heads result?

(1) The player tossed the coin 24 times.
(2) The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points.

Given: When a player in a certain game tossed a coin a number of times, 4 more heads than tails resulted. Heads or tails resulted each time the player tossed the coin.
Let H = the total number of heads that resulted
Let T = the total number of tails that resulted
So, from the given information we can write: H - T = 4

Target question: What is the value of H?

Statement 1: The player tossed the coin 24 times.
We can write: H + T = 24, which means we now have the following system of equations:
H - T = 4
H + T = 24
Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for H and T, which means we could answer the target question with certainty [although we would never waste precious time on tests they actually performing the necessary calculations]
Statement 1 is SUFFICIENT

Statement 2: The player received 3 points each time heads resulted and 1 point each time tails resulted, for a total of 52 points
We can write: 3H + 1T = 52, which means we now have the following system of equations:
H - T = 4
3H + 1T = 52
Since we have a system of 2 different linear equations with 2 variables, we COULD solve the system for H and T, which means we could answer the target question with certainty
Statement 2 is SUFFICIENT

Cheers,
Brent
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Re: When a player in a certain game tossed a coin a number of [#permalink]
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Re: When a player in a certain game tossed a coin a number of [#permalink]
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