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When playing a coin-tossing game, Tom wins $5 when the coin

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by Max@Math Revolution » Mon Aug 12, 2019 11:45 pm

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[GMAT math practice question]

When playing a coin-tossing game, Tom wins $5 when the coin lands on heads and loses $3 when the coin lands on tails.
After tossing the coin 20 times Tom has won a total of $12. How many times did the coin land on heads?

A. 7
B. 8
C. 9
D. 10
E. 11
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by Scott@TargetTestPrep » Wed Aug 14, 2019 4:29 pm
Max@Math Revolution wrote:[GMAT math practice question]

When playing a coin-tossing game, Tom wins $5 when the coin lands on heads and loses $3 when the coin lands on tails.
After tossing the coin 20 times Tom has won a total of $12. How many times did the coin land on heads?

A. 7
B. 8
C. 9
D. 10
E. 11
Letting H = the number of times that Heads came up and T = the number of times that Tails came up, we can create the equations:

H + T = 20

T = 20 - H

and

Since he won $5 each time Heads came up and lost $3 each time Tails came up, we can create the equation for the amount of money he won as:

5H - 3T = 12

Substituting, we have:

5H - 3(20 - H) = 12

5H - 60 + 3H = 12

8H = 72

H = 9

Answer: C

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by Max@Math Revolution » Thu Aug 15, 2019 5:29 pm
=>

Let h be the number of times the coin landed on heads.
Then 20 - h is the number of times the coin landed on tails.
Thus, Tom won 5h - 3(20-h) = 8h - 60 dollars.
Since Tom won $12, this gives the equation 8h - 60 = 12. Solving this equation yields 8h = 72 and h = 9.

Therefore, C is the answer.
Answer: C
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