SOLUTION: If John gives Haiz $7, they will have the same amount of money. If Haiz gives John $7, the ratio of the amount of money he has to the ratio of the money John has will be 1:2. How m

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Question 145551: If John gives Haiz $7, they will have the same amount of money. If Haiz gives John $7, the ratio of the amount of money he has to the ratio of the money John has will be 1:2. How much money has each of them at first?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If John gives Haiz $7, they will have the same amount of money. If Haiz gives John $7, the ratio of the amount of money he has to the ratio of the money John has will be 1:2. How much money has each of them at first?
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Let the original amts be; J and H
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Write an equation for the two statements,
:
"If John gives Haiz $7, they will have the same amount of money."
J - 7 = H + 7
J = H + 7 + 7
J = H + 14
:
" If Haiz gives John $7, the ratio of the amount of money he has to the ratio of the money John has will be 1:2."
%28%28H-7%29%29%2F%28%28J%2B7%29%29 = 1%2F2
Cross multiply:
J+7 = 2(H-7)
J+7 = 2H - 14
J = 2H - 14 - 7
J = 2H - 21
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Substitute (H+14) for J
H + 14 = 2H - 21
14 + 21 = 2H - H
H = $35
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From the 1st equation
J = 35 + 14
J = $49
:
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Check solution in both statements:
"If John gives Haiz $7, they will have the same amount of money."
49 - 7 = 35 + 7
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If Haiz gives John $7, the ratio of the amount of money he has to the ratio of the money John has will be 1:2.
35 - 7 = 28
49 + 7 = 56