SOLUTION: Ron and Ginny each had a certain number of playing marbles. Ron lost a game to Ginny and had to give Ginny half of his marbles. In the second game, Ginny lost and had to give three

Question 197601: Ron and Ginny each had a certain number of playing marbles. Ron lost a game to Ginny and had to give Ginny half of his marbles. In the second game, Ginny lost and had to give three-fourths of her marbles to Ron, who now had thirty marbles. how many marbles did each have originally if Ron had twice as many marbles as Ginny at the start? Explain and show all work to receive full credit.
I've been trying this problem but i have no work i dont know where to start or how to set up the equation.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Ron and Ginny each had a certain number of playing marbles. Ron lost a game to Ginny and had to give Ginny half of his marbles. In the second game, Ginny lost and had to give three-fourths of her marbles to Ron, who now had thirty marbles. how many marbles did each have originally if Ron had twice as many marbles as Ginny at the start? Explain and show all work to receive full credit.
I've been trying this problem but i have no work i dont know where to start or how to set up the equation.
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Keep track of each step of the problem.
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Start:
Ron has "R" marbles
Ginny has "G" marbles
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After 1st Game where Ron lost to Ginny and had to give Ginny half of his marbles.
Ron has (1/2)R
Ginny has G + (1/2)R
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After the 2nd game where Ginny lost and had to give three-fourths of her marbles to Ron, who now had thirty marbles.
Ron has (1/2)R + (3/4)[G + (1/2)R]
Ginny has (we don't care)
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Solve for R and G based on the following information:
Ron now had thirty marbles. How many marbles did each have originally if Ron had twice as many marbles as Ginny at the start?
Equations:
R = 2G
(1/2)R + (3/4)[G + (1/2)R] = 30
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Do some simplifying to get:
R = 2G
2R + 3[G + (1/2)R] = 120
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Substitute to solve for G:
4G + 3(G + G) = 120
10G = 120
G = 12 marbles (original # for Ginny)
R = 2G = 24 marbles (original # for Ron)
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Cheers,
Stan H.
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