P5 Math: Samantha and Megan

Samantha and Megan have some money. If Samantha spends $60 each day and Megan spends $120 on each day, Samantha will have $680 left when Megan has spent all her money. If Samantha spends $120 each day and Megan spends $60 on each day, Samantha will have $140 left when Megan has spent all her money.

How much money does each girl have?

Solution:

Please take note that each girl has FIXED amount of money.
But the number of days on each scenario is different.
For example:

• on scenario 1 there are D spending days
• on scenario 2 there are E spending days

Scenario 1:
============
S: 60D + 680
M: 120D

Scenario 2:
============
S: 120E + 140
M: 60E

Since amount of money of each girl is not changed:

S: 60D + 680 = 120E + 140 (1)
M: 120D = 60E (2)

From (2): 1E = 2D (number of days on scenario 2 is two times number of days in scenario 1)

From (1): 
60D + 680 = 120E + 140
60D + 680 = 240D + 140
D = 3

So D equals to 3 days, or E equals to 6 days.

Samantha has 60D  +680 = $860
Megan has 120D = $360