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?
w-9 = m+9
(m-9)/(w+9) = 1/2
Now, solve for w:
m=w-18, so
(w-18-9)/(w+9) = 1/2
2w-54 = w+9
w = 63
check:
m=63-18 = 45
(45-9)/(63+9) = 36/72 = 1/2
To solve this problem, let's assign variables to represent the amounts of money Will and Molly have.
Let's say "w" represents the amount of money Will has, and "m" represents the amount of money Molly has.
According to the information given:
1) If Will gives Molly $9, he will have the same amount of money as her.
This can be expressed as: Will's money - $9 = Molly's money + $9
Algebraically, this is: w - 9 = m + 9
2) If Molly gives Will $9, the ratio of the money she has to the money Will has will be 1 : 2.
This can be expressed as: Molly's money - $9 = (Will's money + $9) * 2
Algebraically, this is: m - 9 = (w + 9) * 2
Now, we have a system of two equations with two variables. We can solve this system to find the values of "w" and "m".
Let's start by simplifying equation (1):
w - 9 = m + 9
w = m + 18 --------------(3)
Now, substitute equation (3) into equation (2):
m - 9 = (w + 9) * 2
m - 9 = ((m + 18) + 9) * 2
m - 9 = (m + 27) * 2
m - 9 = 2m + 54
m - 2m = 54 + 9
-m = 63
m = -63 (dividing both sides by -1 changes the sign)
Since Molly's money cannot be negative in this context, we can conclude that there is no valid solution for this problem.