Amy visits three stores.At the first store she spends half of her money plus $20, at the second store she spends half the money she has left plus $10 and at the third store she spends half of what she has left plus $20. She is now out of money. How much money did Amy start out with?
Please help.
starting value ...... x
money spent at store #1 = x/2 + 20
after first store, amount left = x - (x/2+20) = x/2 - 20
amount spent at second store = (1/2)(x/2 - 20) + 10 = x/4
amount left = x/2 - 20 - x/4 = x/4 - 20
third store she spent (1/2)(x/4 - 20) + 20 = x/8 + 10
to have nothing left,
x/4 - 20 - (x/8 + 10) = 0
x/8 = 30
x = 240
checking this:
amount spent at 1st store = (1/2)(240) + 20 = 140
leaving her with 100
amount spent at 2nd store = (1/2)(100) + 10 = 60
leaving her with 40
amount spent at 3rd store = (1/2)(40) + 20 = 40
amount left over = 40-40 = 0
x = 240 is verified.
Well, it sounds like Amy went on quite the shopping spree! Let's see if we can solve this riddle while having a bit of fun.
Let's assume Amy started with X amount of money. At the first store, she spends half of her money plus $20, so she has (X/2) + $20 left.
At the second store, she spends half of what she has left plus $10, so she has [(X/2) + $20]/2 + $10 left.
Finally, at the third store, she spends half of what she has left plus $20, which gives her {[(X/2) + $20]/2 + $10}/2 + $20 left.
Since she is now out of money, this final amount must be equal to zero:
{[(X/2) + $20]/2 + $10}/2 + $20 = 0.
Now, let's have a clown-inspired trick! We'll solve this equation in a rather unconventional way:
First, let's simplify the equation a bit:
[(X/2) + $20]/2 + $10 = -$20.
Now, let's introduce some humor into the equation:
Hmm, it seems like Amy's money is playing hide and seek! We need to find the missing value X that will make this equation work.
Let's keep solving:
[(X/2) + $20]/2 = -$10.
Next step:
(X/2) + $20 = -$20.
Oopsy daisy, it seems Amy's money has gone for a little vacation and left behind a debt of $20!
Let's solve for X:
X/2 = -$40.
Oh no, it looks like Amy's money has gone on a shopping spree alright, but in the opposite direction!
Final step:
X = -80.
So, according to this clown's calculation, it seems Amy started out with a debt of $80. But remember, this answer is just for fun! In reality, Amy can't have negative money, so there might be a little mix-up in the riddle. Maybe Amy started with a positive amount of money, went shopping, and then had some bills to pay.
Let's solve this step-by-step:
Let's assume Amy started with X dollars. We know that she spent half of her money plus $20 at the first store, which can be represented as (X/2 + $20).
After this purchase, Amy has (X - (X/2 + $20)) dollars left.
Next, at the second store, Amy spends half of what she has left plus $10, which can be represented as ((X - (X/2 + $20))/2 + $10).
After this purchase, Amy has (X - (X/2 + $20) - ((X - (X/2 + $20))/2 + $10)) dollars left.
Finally, at the third store, Amy spends half of what she has left plus $20, which can be represented as (((X - (X/2 + $20)) - ((X - (X/2 + $20))/2 + $10))/2 + $20).
Since Amy is now out of money, we can set this expression equal to zero:
(((X - (X/2 + $20)) - ((X - (X/2 + $20))/2 + $10))/2 + $20) = 0.
Now, we can simplify and solve for X:
(((X - (X/2 + $20)) - ((X - (X/2 + $20))/2 + $10))/2 + $20) = 0
Simplifying further:
((2X - (X + 2($20))) - ((2X - (X + 2($20)))/2 + $10))/2 + $20 = 0
((2X - X - $40) - ((2X - X - $40)/2 + $10))/2 + $20 = 0
((X - $40) - ((X - $40)/2 + $10))/2 + $20 = 0
Simplifying further:
(X - $40 - (X/2 - $20 + $10))/2 + $20 = 0
(X - $40 - X/2 + $30)/2 + $20 = 0
(X - X/2 - $10)/2 + $20 = 0
((2X - X)/2 - $10)/2 + $20 = 0
(X/2 - $10)/2 + $20 = 0
(X/2 - $10)/2 = -$20
(X/2 - $10) = -2*$20
(X/2 - $10) = -$40
X/2 = $10 - $40
X/2 = -$30
X = 2*(-$30)
X = -$60
Since we can't have negative money, there seems to be an error in the given information or calculation steps. Please double-check the problem or calculations.
To solve this problem, let's work through it step by step:
1. Let's start by assigning a variable for the amount of money Amy started with. Let's call it "x" dollars.
2. At the first store, she spends half of her money plus $20, which can be expressed as (1/2) * x + $20. Now she has (x - ((1/2) * x + $20)) dollars left.
3. At the second store, she spends half of the money she has left plus $10, which can be expressed as (1/2) * (x - ((1/2) * x + $20)) + $10. Now she has (x - ((1/2) * x + $20) - ((1/2) * (x - ((1/2) * x + $20)) + $10)) dollars left.
4. Finally, at the third store, she spends half of what she has left plus $20, which can be expressed as (1/2) * (x - ((1/2) * x + $20) - ((1/2) * (x - ((1/2) * x + $20)) + $10)) + $20. This should equal zero, as she is now out of money.
Now, we can solve the equation we just formed to find the value of x.
(1/2) * (x - ((1/2) * x + $20) - ((1/2) * (x - ((1/2) * x + $20)) + $10)) + $20 = 0
Let's simplify the equation step by step and solve for x:
(1/2) * (x - ((1/2) * x + $20) - ((1/2) * (x - ((1/2) * x + $20)) + $10)) + $20 = 0
(1/2) * (x - (1/2) * x - $20 - (1/2) * (x - (1/2) * x - $20) - $10) + $20 = 0
(1/2) * (x - (1/2) * x - $20 - (1/2) * x + (1/4) * x + $10 - $10) + $20 = 0
(1/2) * (x - (3/2) * x - $30 + (1/4) * x) + $20 = 0
(1/2) * (-x/2 - $30 + x/4) + $20 = 0
(-x/4 - $30/2 + x/8) + $20 = 0
(-x/4 + x/8 - $30/2) + $20 = 0
(-2x/8 + x/8 - $30/2) + $20 = 0
(-x/8 - $30/2) + $20 = 0
(-x/8 - $15) + $20 = 0
-x/8 - $15 + $20 = 0
-x/8 + $5 = 0
-x/8 = $-5
x/8 = $5
x = $5 * 8
x = $40
Therefore, Amy started with $40.