If Will gives Molly $9 dollars he will have the same amount of money as her. If Molly give Will $9, the ratio of money she has to the money will has will be 1:2. How much money does will have in the beginning?
Can you give me an explanation of each step, please? I'm having a hard time determining what to do. Thanks :)
RUSSEL
Sure! Let's break down the problem step by step.
Step 1: Assign variables.
Let's assume that Will's initial amount of money is represented by 'W' dollars, and Molly's initial amount of money is represented by 'M' dollars.
Step 2: Analyze the given information.
The first statement states that if Will gives Molly $9, they will have the same amount of money. This can be expressed as: W - 9 = M + 9.
The second statement states that if Molly gives Will $9, the ratio of her remaining money to Will's remaining money will be 1:2. This can be expressed as: (M - 9) / (W + 9) = 1/2.
Step 3: Solve the equations simultaneously.
To find the initial amount of money Will has, we need to eliminate the variables 'M' and 'W'. We'll start by rearranging the first equation to solve for 'M': M = W - 18.
Substituting this value of 'M' into the second equation gives us: (W - 18 - 9) / (W + 9) = 1/2.
Step 4: Solve for 'W'.
Now, let's simplify the equation and solve for 'W'.
(W - 27) / (W + 9) = 1/2.
Cross-multiply: 2(W - 27) = W + 9.
Expand and solve: 2W - 54 = W + 9.
Subtract 'W' from both sides: 2W - W = 9 + 54.
Simplify: W = 63.
Therefore, Will initially has $63.
Step 5: Check the answer.
To ensure the solution is correct, we can substitute the value of 'W' back into the equation M = W - 18.
M = 63 - 18 = 45.
So, Molly initially has $45.
Step 6: Verify the solution.
Let's check if the conditions given in the problem are satisfied.
If Will gives Molly $9, Will will have $63 - $9 = $54, and Molly will have $45 + $9 = $54. This matches the first condition.
If Molly gives Will $9, the ratio of her remaining money ($45 - $9 = $36) to Will's remaining money ($63 + $9 = $72) is indeed 1:2.
Therefore, our solution is correct. Will initially has $63.