During a shopping trip, Cindy spent half of her money in the first shop. She spent $2 more than half of her remaining money in the second shop. She
was left with $30 in the end. How much money did Cindy have at first?
how to do this
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Let's use algebra to solve this problem step-by-step.
Let's represent the amount of money Cindy had at first as "x".
Step 1: Cindy spent half of her money in the first shop.
So, she spent x/2 in the first shop.
Step 2: After spending in the first shop, Cindy had x - (x/2) = x/2 left.
Step 3: Cindy spent $2 more than half of her remaining money in the second shop.
So, she spent (x/2) + $2 in the second shop.
Step 4: After spending in the second shop, Cindy had (x/2) - ((x/2) + $2) = (x/2) - (x/2) - $2 = -$2 left.
Step 5: Cindy was left with $30 in the end.
So, (x/2) - $2 = $30.
Step 6: Let's solve the equation to find the value of x.
(x/2) - $2 = $30
(x/2) = $30 + $2
(x/2) = $32
x = 2 * $32
x = $64
Therefore, Cindy had $64 at first.
To solve this problem, let's work step by step:
Step 1: Let's assume the amount of money Cindy had at first as 'x'.
Step 2: Cindy spent half of her money in the first shop, so she has (x/2) money remaining.
Step 3: Cindy spent $2 more than half of her remaining money in the second shop, which means she spent ((x/2) + $2).
Step 4: After spending money in the second shop, Cindy was left with $30, so her remaining money is (x/2) - ((x/2) + $2) = $30.
Step 5: Simplifying the equation, we have (x/2) - (x/2) - $2 = $30.
Step 6: Combining like terms, we get -$2 = $30.
Step 7: This equation is not possible, as we cannot have a negative amount of money. Therefore, there is no solution to this problem.
In conclusion, there is no amount of money Cindy could have had at first that would satisfy the given conditions.