If Owen gives $40 to Charley, the will have an equal amount of money. If Charley gives $80 to Owen, the ratio of Owen's money to Charley's money will be 4-1.How much money does Owen have in the beginning?
Work: I don't have much but
X=Owen
C=charley
X=C-40
4C=O+80
not quite
If they start out with o and c dollars, then
o-40 = c+40
4(c-80) = o+80
rearrange things a bit and you have
o-c = 80
o-4c = -400
3c = 480
c = 160
now find o
0=240
Let's solve the equations step-by-step to find the amount of money Owen has in the beginning.
Step 1: Given information
Owen gives $40 to Charley, so Owen has x - 40 dollars.
Charley gives $80 to Owen, so the ratio of Owen's money to Charley's money is 4:1.
Step 2: Setting up the equations
We can write the equations based on the given information:
x - 40 = c
4c = x + 80
Step 3: Solving the equations
We can substitute the value of x - 40 from the first equation into the second equation for x:
4c = (x - 40) + 80
4c = x + 40
Step 4: Substituting x from the first equation into the second equation
4c = (c + 40) + 40
4c = c + 80
Step 5: Simplifying the equation
4c - c = 80
3c = 80
Step 6: Solving for c
Dividing both sides of the equation by 3, we get:
c = 80 / 3
c ≈ 26.67
Step 7: Solving for x
Using the value of c, we can substitute it back into the first equation:
x - 40 = 26.67
x = 26.67 + 40
x ≈ 66.67
Therefore, Owen has approximately $66.67 in the beginning.
To find out how much money Owen had in the beginning, we can use the information given and set up a system of equations.
Let's denote Owen's initial amount of money as X and Charley's initial amount of money as C.
From the first statement, we know that if Owen gives $40 to Charley, they will have an equal amount of money. This can be represented as:
X - 40 = C ----(1)
From the second statement, we know that if Charley gives $80 to Owen, the ratio of Owen's money to Charley's money will be 4:1. This can be represented as:
4C = X + 80 ----(2)
Now we have a system of equations consisting of equations (1) and (2). We can solve this system of equations to find the value of X (Owen's initial amount of money).
We can solve this system using the substitution method. First, we will solve equation (1) for X in terms of C:
X = C + 40
Now we substitute this expression for X in equation (2):
4C = (C + 40) + 80
Now we simplify the equation to solve for C:
4C = C + 120
3C = 120
C = 40
Now that we have found the value of C, we can substitute it back into equation (1) to find X:
X - 40 = 40
X = 80
Therefore, Owen initially had $80.