Lily and Mackenzie collected some stamps. If Lily gave 4 stamps to Mackenzie, Mackenzie would have twice as many stamps as Lily. If Mackenzie gave 4 stamps to Lily, they would have the same number of stamps. How many stamps did each girl have?
L-4 = (1/2)(M+4)
M-4 = L+4
2 L - 8 = M + 4
L = M-8
2 (M-8) - 8 = M + 4
2 M - 24 = M + 4
M = 28
L= 20
Thanks so much!
You are welcome.
To solve this problem, let's use algebraic equations.
Let's assume that Lily has "L" stamps and Mackenzie has "M" stamps.
From the first statement, "If Lily gave 4 stamps to Mackenzie, Mackenzie would have twice as many stamps as Lily," we can express this as:
M + 4 = 2(L - 4)
From the second statement, "If Mackenzie gave 4 stamps to Lily, they would have the same number of stamps," we can express this as:
L + 4 = M - 4
Now we have a system of two equations with two variables:
M + 4 = 2(L - 4)
L + 4 = M - 4
Let's solve the system of equations step by step.
1. Expand the equations:
M + 4 = 2L - 8
L + 4 = M - 4
2. Rearrange the equations to isolate one variable:
M - 2L = -12
L - M = -8
3. Add the two equations together:
(M - 2L) + (L - M) = -12 + (-8)
-M + L - 2L = -20
-3L = -20
4. Solve for L:
L = (-20) / (-3)
L = 20 / 3
5. Substitute the value of L into one of the original equations to solve for M:
M + 4 = (2 * 20 / 3) - 8
M + 4 = 40 / 3 - 24 / 3
M + 4 = 16 / 3
M = 16 / 3 - 4
M = 16 / 3 - 12 / 3
M = 4 / 3
So, Lily has 20/3 stamps, which is approximately 6.67 stamps, and Mackenzie has 4/3 stamps, which is approximately 1.33 stamps.