+0  
 
0
110
2
avatar

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?

 Feb 20, 2022
 #1
avatar
+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

 Feb 21, 2022
 #2
avatar+231 
+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

 Feb 21, 2022

45 Online Users

avatar
avatar