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?

Guest Feb 20, 2022

#1**+1 **

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**

Guest Feb 21, 2022

#2**+1 **

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

Slimesewer Feb 21, 2022