Laura, Tim and Ken had $360 altogether. Laura gave half of her money to Tim. Tim then gave 3/7 of his money to Ken. Ken then gave 2/5 of his money to Laura. The three of them had the same amount of money in the end. How much money did each of them have at first?
L==Laura, T==Tim, K==Ken
L - 1/2L ==1/2L - what L has left
T + 1/2L ==What T has now.
[T + 1/2L] x 3/7 ==3/7T + 3/14L - What T gave to K
K + 3/7T + 3/14L ==What K has now
4/7T + 4/14L ==What T has left...................................................(Equation 1)
[K + 3/7T + 3/14L] x 2/5==2/5K + 6/35T + 6/70L ==What K gave to L
2/5K + 6/35T + 6/70L + 1/2L ==What L has now........................(Equation 2)
3/5K + 9/35T + 9/70L ==What K has now....................................(Equation 3)
4/7T + 4/14L ==120................................(Equation 1)
[2/5K + 6/35T + 41/70L]==120...............(Equation 2)
[3/5K + 9/35T + 9/70L]==120.................(Equation 3)
Use, additions or subtractions or substitutions to get:
K ==110 - What Ken started with
L ==80 - What Laura started with
T==170 - What Tim started with
+237 I will use backward approach.
At last, all three of them had
Same amount of money.
So, All of them had $360/3 = $120
Before the end, Ken gave 2/3 of his money to Laura. So, 3/5 of Ken's money = $120
| Laura $120 | Tim $120 | Ken $120 <-- (End Step) |
| $40 | $120 | $200 <-- (Previous Step) |
| $40 | $210 | $110 --> (Step II) |
| $80 | $170 | $110 --> (Initially) |
Ken's money in Previous Step = $200, Ken gave $80 to Laura. So, Laura's money in Previous Step = $(120 - 80) = $40
Step 2: - Tim gave 3/7 of his money to Ken.
So, 4/7 of Tim's money = $120
Tim's money in Step 2 = $210
Ken's money in Step 2 = $200 - $90 = $110 because Tim gave $90 to Ken.
Initially --> Laura gave half her money to Tim.
So, Laura's money initially = $40 * 2 = $80.
Tim's money initially = $(210 - 40) = $170
And, Ken's money initially = $110
