Felix, grace and Kristin share a sum of money. 40% of Felix's money is equal to 25% of graces share. Kristin's share is one third of graces share. If Felix gives $24 to Kristin, Kristin's share will increase by 25%. Find each person's share.
Let's assume the total sum of money shared is $x.
According to the given information:
0.4F = 0.25G
G = 3K
From the first equation, we get:
F = 0.25G / 0.4
F = 0.625G
Substitute F and G into the sum equation:
F + G + K = x
0.625G + G + 3K = x
1.625G + 3K = x
Given that if Felix gives $24 to Kristin, Kristin's share will increase by 25%, we can set up the following equation:
1.25(3K + 24) = 3K
Solving for K, we get:
3.75K + 30 = 3K
0.75K = -30
K = -40
Substitute K back into the equations to find F and G:
F = 0.625(-40) = -25
G = 3(-40) = -120
Now, we ignore the negative signs as they are due to the assumptions and calculations made. So, each person's share is:
Felix: $25
Grace: $120
Kristin: $40