Simultaneous Buck

Algebra Level 2

In a game of chance, a gambler speaks privately to two persons. To one he says, ''If you win, I will give you thrice your stake money , else you will give me four times of that.'' Going to the other, the gambler promises to give him five times his stake money , if he wins but he will have to give seven times of the same on losing. From both of them, the gambler will gain $ 65 \$65 . Find the sum of their prize money .

65 485 355 95

Shubhrajit Sadhukhan by Shubhrajit Sadhukhan , 16, India

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2 solutions

Relevant Wiki: Simultaneous Equations

Let their stake money be x x and y y , respectively.

Case 1: If the first person wins, the gambler gets 7 times the stake money of the second person and rewards 3 times the stake money to the first person. So, he has:

7 y − 3 x = 65 7y - 3x = 65

Case 2: If the second person wins, the gambler gets 4 times the stake money of the first person and rewards 5 times the stake money to the second person. So, he has:

4 x − 5 y = 65 4x - 5y = 65

By solving with a suitable method,

x = $ 60 x = \$60

y = $ 35 y = \$35

So, the sum of the prize money

= 3 x + 5 y = 3x + 5y

= $ 355 = \boxed{\$ 355}

4 Helpful 3 Interesting 3 Brilliant 0 Confused

This is how I solved that.

A Former Brilliant Member - 11 months, 3 weeks ago

25%+luck!!!!!!!!!!

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