Samantha smith went into a store and spent half her money and then spent $20 more. Samantha then went into a second store and spent half her remaining money and then spent $20 more. After spending money in the second store, Samantha had no money left. How much money did she have when she went into the first store?
Let x = original amount of money.
1/2x - 20 - (1/2)(1/2x-20) - 20 = 0
Solve for x.
couldnt it be any number
Let's assume Samantha had "M" dollars when she went into the first store.
She spent half her money and then spent $20 more, which means she spent (M/2) + $20 in the first store.
After spending money in the first store, she had (M - ((M/2) + $20)) dollars remaining.
She went into the second store and spent half her remaining money, which is (M/2) - (((M/2) + $20)/2) dollars.
Then she spent $20 more in the second store, which means she spent (M/2) - (((M/2) + $20)/2) + $20 dollars in the second store.
After spending money in the second store, Samantha had no money left. This means her remaining money is 0.
So, we can write the equation:
(M - ((M/2) + $20)) - (((M/2) + $20)/2) + $20 = 0
Solving this equation will give us the value of M, which is the amount of money Samantha had when she went into the first store.
To determine how much money Samantha had when she went into the first store, we can follow these steps:
Step 1: Let x represent the amount of money Samantha had initially.
Step 2: Samantha spent half her money in the first store, which is (1/2)x.
Step 3: After spending half her money, Samantha had (1/2)x remaining.
Step 4: Samantha spent $20 more, so her remaining money after the first store is (1/2)x - $20.
Step 5: Samantha went into the second store and spent half her remaining money, which is (1/2)((1/2)x - $20).
Step 6: After spending half her remaining money in the second store, Samantha had ((1/2)x - $20)/2 remaining.
Step 7: Samantha spent $20 more in the second store, and had no money left.
Step 8: Equating the remaining money to $0, we have ((1/2)x - $20)/2 - $20 = 0.
Step 9: Simplify and solve for x.
Let's solve it together:
((1/2)x - $20)/2 - $20 = 0
(1/2)x - $40 - $40 = 0
(1/2)x - $80 = 0
(1/2)x = $80
x = $80 * 2 = $160
Therefore, Samantha had $160 when she went into the first store.