If Will gives Molly $9, he will have the same amount of money as her. If Molly gives Will $9, the ratio of the money she has to the money Will has will be 1 : 2. How much money does Will have in the beginning?
Molly's original amount ---- x
Will's original amount ------y
after give-away:
Molly has x+9
Will has y-9
but then x+9 = y-9
y = x+18
after hypothetical other case:
Molly has x-9
Will has y+9
(x-9)/(x+9) = 1/2
2x - 18 = y+9
y = 2x - 27
so 2x - 27 = x + 18
x = 45 , then y = 63
check:
after 1st giveaway:
Molly has x+9 = 45+9 = 54
Will has y - 9 = 63-9 =54 , they have the same
after 2nd giveaway:
Molly has x-9 = 45-9 = 36
Will has y + 9 = 63+9 = 72 , which is twice the 36
To solve this problem, we can set up a system of equations based on the given information.
Let's suppose the amount of money Will has in the beginning is 'x' dollars.
Since Molly currently has more money than Will, we know that Molly has 'x + 9' dollars.
According to the first condition, if Will gives Molly $9, then their amounts of money will be the same. So, Will will have 'x - 9' dollars and Molly will have 'x + 9 + 9' dollars.
According to the second condition, if Molly gives Will $9, the ratio of Molly's money to Will's money will be 1:2. So, we can set up the equation:
(x + 9 - 9) / (x - 9 + 9) = 1/2
Simplifying this equation, we have:
x / x = 1/2
Since any number divided by itself is 1, this equation simplifies to:
1 = 1/2
This is not a true statement, which means there is no solution. Therefore, the problem is inconsistent and there is no exact amount of money that Will has in the beginning that satisfies all the given conditions.