Daniel has $160 more than Alex. After giving 1/10 of his money to Alex, he now has 3 times as much money than Alex. How much money do they have in the first place?

Ref: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=1774#p1774

Daniel has $160 more than Alex. After giving 1/10 of his money to Alex, he now has 3 times as much money than Alex. How much money do they have in the first place?

Ref: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=1774#p1774

alfretztay

After —

Daniel : 9 units

Alex : 3 units

At first —

Daniel : 10 units

Alex : 2 units

10 units – 2 units = 8 units = 160

1 unit = 20

9 units + 3 units = 12 units = 12 x 20 = 240

Ans : $240.

Onetuition

at beginning, Daniel has 10u

after Daniel give Alex 1 u,

now, Daniel has 9u, and Alex has 3 u ( Daniel has 3 times more than Alex)

so at the beginning, Alex has 2u, so 10u – 2u = 160, 1u is 20

rong50

D-A=160

A = D-160

(9/10)D = 3(A+[1/10]D)

(9/10)D = 3([D-160]+[1/10]D)

(9/10)D = 3D – 480 + [3/10] D

480 = 12/5 D

D = 200

A = 200-160 = 40

qingni0000

1) d = a + 160

2) 0.9d = (a + 0.1d) * 3

d = 5a

4a = 160

a = 40

d =200

thelucidoperatives

Before :

Daniel : 10 units + $160

Alex : 10 units

After :

Daniel : 3 parts

Alex : 1 part

Since Daniel gives 1/10 to Alex, he has given (1 unit + $16) to Alex

In the “After” model,

1 part (for Alex) = 11 units + $16

3 parts (for Daniel) = 9 units + $144 ; ie. 1 part for Daniel is 3 units + $48

The difference is 2 parts : this is the key

2(11units + 16) = 6 units + $96

22 units + $32 = 6 units + $96

16 units = $64

1 unit = $4

At first,

Alex has 10 units = 10 X $4 = $40

Daniel has 10 units + $160 = $40 + $160 = $200.

askq-editor

askq-editor

Not sure how to draw model here. Need to have before and after model.

Before :

Daniel : 10 units + $160

Alex : 10 units

After :

Daniel : 3 parts

Alex : 1 part

Since Daniel gives 1/10 to Alex, he has given (1 unit + $16) to Alex

In the “After” model,

1 part (for Alex) = 11 units + $16

3 parts (for Daniel) = 9 units + $144 ; ie. 1 part for Daniel is 3 units + $48

The difference is 2 parts : this is the key

2(11units + 16) = 6 units + $96

22 units + $32 = 6 units + $96

16 units = $64

1 unit = $4

At first,

Alex has 10 units = 10 X $4 = $40

Daniel has 10 units + $160 = $40 + $160 = $200.

Ref: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=1814#p1814