Lets x = the amount Sheila's deposit each time
So 6 deposits = 6x
Sheila's sister deposits was $10 more each deposit Sheila made, then her sister deposit amount each time should be: x +10
Sheila's sister made 5 deposits: 5(x+10)
Both sisters deposited the same amount in the end:
6x = 5(x+10)
6x = 5x + 50
Now you can add (-5x) to both sides:
6x + (-5x) = 5x + 50 + (-5x)
6x - 5x = 5x + 50 - 5x
Simplify both sides:
x = 50
So Sheila deposits each time: $50
Sheila's sister deposits each time: x + 10 = 50 +10 = 60
Double check:
Sheila deposits 6 times = 6 x 50 = 300
Sheila's sister deposits 5 times = 60 x 5 = 300
Both deposited $300 (same amount) in the end.