to start,
Tim had x
Sally had y
after game 1,
Tim had 2/5 x - 7
Sally had y + 3/5 x + 7
after game 2,
Sally had 3/4 (y + 3/5 x + 7) - 4 = 3/4 y + 9/20 x + 5/4
Tim had 2/5 x - 7 + 1/4 (y + 3/5 x + 7) + 4 = 11/20 x + 1/4 y - 5/4
after game 3,
Tim had 1/3 (11/20 x + 1/4 y - 5/4) = 11/60 x + 1/12 y - 5/12
Sally had (3/4 y + 9/20 x + 5/4) + 2/3 (11/20 x + 1/4 y - 5/4) = 11/12 y + 49/60 x + 5/12
so we are left with
11x + 5y = 3685
49x + 55y = 21095
solve that to get
x = 270
y = 142 <--- Sally
Tim and Sally were playing marbles. In the first game, Tim lost 3/5 of what he had and another 7 more marbles to Sally. In the second game, Sally lost 1/4 of what she had and another 4 marbles to Tim. In the third game, Tim lost 2/3 of what he had to Sally. At the end of three games, Tim had 61 marbles and Sally had 352 marbles. How many marbles did Sally have at first?
1 answer
2 answers