in a game of chips, pauli lost half her chips in the first round, won 236 chips, then lost half her total, and finally won 71 chips. she finished with 241 chips. how many chips did she have at the beginning of the game
Let's break down the given information step by step:
In the first round, Pauli lost half her chips. Let's call her initial number of chips x. Therefore, she lost x/2 chips.
After losing half her chips, Pauli won 236 chips. We can now calculate her total number of chips after the first round: x - (x/2) + 236.
In the next round, she lost half her total number of chips. After the first round, she had (x - (x/2) + 236) chips. Therefore, her number of chips after losing half is: (x - (x/2) + 236)/2.
Finally, she won 71 chips which brings her total number of chips to 241. We can now make an equation to solve for x:
[(x - (x/2) + 236)/2] + 71 = 241
Simplifying the equation:
(x - (x/2) + 236)/2 = 241 - 71
(x - (x/2) + 236)/2 = 170
x - (x/2) + 236 = 340
x - (x/2) = 340 - 236
x - (x/2) = 104
(2x - x)/2 = 104
x/2 = 104
x = 104 * 2
x = 208
Therefore, Pauli had 208 chips at the beginning of the game.
Let's break down the information step by step to find out how many chips Pauli had at the beginning of the game.
Step 1: Pauli lost half her chips in the first round.
Let's represent the number of chips Pauli had after losing half as "x/2".
Step 2: Pauli won 236 chips.
Now the total number of chips Pauli has is "x/2 + 236".
Step 3: Pauli lost half her total chips.
After losing half of her chips again, the number of chips Pauli has is "(x/2 + 236)/2".
Step 4: Pauli won 71 chips.
Now the total number of chips Pauli has is "(x/2 + 236)/2 + 71".
Step 5: She finished with 241 chips.
According to the given information, we have the equation:
"(x/2 + 236)/2 + 71 = 241".
Let's solve this equation to find the value of x and determine the initial number of chips:
(x/2 + 236)/2 + 71 = 241
(x/2 + 236)/2 = 241 - 71
(x/2 + 236)/2 = 170
x/2 + 236 = 340
x/2 = 340 - 236
x/2 = 104
x = 2 * 104
x = 208
Therefore, Pauli initially had 208 chips at the beginning of the game.