the ratio of Mark's shirt to edwin's shirts is 3:5. if Mark gives Edwin 7 shirts and the ratio becomes 1:3, how many shirts did each have at first?
m/e = 3/5
(m-7)/(e+7) = 1/3
Now just solve for m and e.
To solve this problem, we'll need to use a method called "Ratio Manipulation."
Let's start by assigning variables to the number of shirts Mark and Edwin had initially.
Let M represent the number of shirts Mark had initially, and let E represent the number of shirts Edwin had initially.
According to the given information, the ratio of Mark's shirts to Edwin's shirts is 3:5. This can be expressed as:
M/E = 3/5
Next, we're told that Mark gives Edwin 7 shirts and the new ratio becomes 1:3. This means the ratio of Mark's shirts to Edwin's shirts after the exchange is:
(M - 7) / (E + 7) = 1/3
Now we can set up a system of equations to solve for M and E.
We have two equations:
1) M/E = 3/5
2) (M - 7)/(E + 7) = 1/3
To solve this system of equations, we can use the method of substitution or elimination. I'll use substitution here.
From Equation 1, we can rearrange it to solve for M in terms of E:
M = (3/5)E
Now substitute M in Equation 2 with (3/5)E:
[(3/5)E - 7] / (E + 7) = 1/3
Multiply both sides by 3(E + 7) to remove the fractions:
3[(3/5)E - 7] = (E + 7)
Expand and simplify:
(9/5)E - 21 = E + 7
Multiply both sides by 5 to eliminate the fraction:
9E - 105 = 5E + 35
Move variables to one side and constants to the other:
9E - 5E = 35 + 105
4E = 140
Divide both sides by 4 to isolate E:
E = 140 / 4
E = 35
Now that we have E, we can find M by substituting it back into Equation 1:
M = (3/5)E
M = (3/5)(35)
M = 21
Therefore, Mark originally had 21 shirts and Edwin had 35 shirts.