SOLUTION: Hi
A and B had some cards. After A lost 68 cards to B the ratio of cards that A and B had were 3:8 respectively. When B lost 126 cards to A the ratio of cards that A and B had we
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A and B had some cards. After A lost 68 cards to B the ratio of cards that A and B had were 3:8 respectively. When B lost 126 cards to A the ratio of cards that A and B had we
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Question 1176896: Hi
A and B had some cards. After A lost 68 cards to B the ratio of cards that A and B had were 3:8 respectively. When B lost 126 cards to A the ratio of cards that A and B had were 2:3 respectively.
How many cards did A have at first.
Thanks Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source):
A and B had some cards.
After A lost 68 cards to B, the ratio of cards that A had to B was 3/8.
When B subsequently lost 126 cards to A, the ratio of cards that A had to B became 2/3.
the first part of this problem became:
(A - 68) / (B + 68) = 3/8
the second part of this problem became:
(A + 58) / (B - 58) = 2/3.
the reason for this is that A first lost 68 cards and then won 126 cards, giving him a net gain of 58 cards and that B first won 68 cards and then lost 126 cards, giving him a net loss of 58 cards.
you have two equations that need to be solved simultaneously.
they are:
(A - 68) / (B + 68) = 3/8
(A + 58) / (B - 58) = 2/3
in the first equation, you get:
(A - 68) = 3/8 * (B + 68)
solve for A to get:
A = 3/8 * (B + 68) + 68.
in the second equation, you get:
(A + 58) = 2/3 * (B - 58)
solve for A to get:
A = 2/3 * (B - 58) - 58
since they are both equal to A, you get:
3/8 * (B + 68) + 68 = 2/3 * (B - 58) - 58
subtract 3/8 * (B + 68) from both sides of the equation and add 58 to both sides of the equation to get:
68 + 58 = 2/3 * (B - 58) - 3/8 * (B + 68)
simplify to get:
126 = 2/3 * B - 2/3 * 58 - 3/8 * B - 3/8 * 68
add 2/3 * 58 and 3/8 * 68 to both sides of the equation to get:
126 + 2/3 * 58 + 3/8 * 68 = 2/3 * B - 3/8 * B
put everything under the common denominator of 24 to get:
3024 / 24 + 928 / 24 + 612 / 24 = 16/24 * b - 9/24 * B
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Hi
A and B had some cards. After A lost 68 cards to B the ratio of cards that A and B had were 3:8 respectively. When B lost 126 cards to A the ratio of cards that A and B had were 2:3 respectively.
How many cards did A have at first.
Thanks
Let original number A and B had, be A and B, respectively
After A lost 68 cards to B, A had A - 68 remaining, and B then had, B + 68
We then get:
16A - 6B = 1,496 ---- Multiplying eq (i) by 2 ---- eq (iii)
9A - 6B = - 870 ---- Multiplying eq (ii) by 3 --- eq (iv)
7A = 2,366 -------- Subtracting eq (iv) from eq (iii)
Original number A had, or
