N a game of chips, Pauli lost half her chips in the first round, won 54 chips, then lost half her total, and finally won 50 chips. She finished with 157 chips. How many chips did she have at the beginning of the game? Pauli had chips at the beginning of the game.

Pauli had 320 chips at the beginning of the game

Step-by-step explanation:

denoting x as the number of initial chips then

1°) lost half her total = x/2  , remaining after that = x-x/2= x/2

2°) won 54 chips, now Pauli has 54+x/2

3°) lost half her total again , now Pauli has 1/2( 54+x/2)

4°) won 50 chips , finally Pauli has  1/2( 54+x/2) + 50

therefore

1/2( 54+x/2) + 50 = 157

54+x/2 = (157-50)*2 = 214

x/2 = 214-54 = 160

x= 160*2 = 320 chips

x= 320 chips

then Pauli had 320 chips at the beginning of the game

x = 3 ± √(5+y)

here is a big fat