If Will gives Molly $9 he will have the same amount 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
w - m = 18
-w + 2m = 27
m = 45
w = 63
so, we start out will=63, molly=45
63-9 = 54 = 45+9
45-9 = 36 = 1/2 (63+9)
molly=45
Will=63
To solve this problem, we can set up a system of equations.
Let's say the amount of money Will has in the beginning is "x" dollars. And let's say the amount of money Molly has in the beginning is "y" dollars.
According to the first condition, if Will gives Molly $9, he will have the same amount as her. This can be represented as:
x - 9 = y + 9
Simplifying this equation, we get:
x - y = 18 --- (Equation 1)
According to the second condition, if Molly gives Will $9, the ratio of the money she has to the money Will has will be 1:2, which can be represented as:
(y - 9) / (x + 9) = 1 / 2
Cross-multiplying and simplifying this equation, we get:
2(y - 9) = x + 9
2y - 18 = x + 9
2y - x = 27 --- (Equation 2)
We now have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system to find the values of x and y.
To do so, we can solve Equation 1 for x in terms of y:
x = y + 18
Substituting this into Equation 2, we get:
2y - (y + 18) = 27
y - 18 = 27
y = 45
Now that we know the value of y, we can substitute it back into the equation x = y + 18 to find the value of x:
x = 45 + 18
x = 63
Therefore, Will has $63 in the beginning.