Julia spent 1/3 of her money. Then she lost 1/2 of the rest. She now has $10 left. How much did she get for her birthday?
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30
Let's assume that the amount Julia had before spending 1/3 of her money was x dollars.
After spending 1/3 of her money, Julia has 2/3 of her money left.
Let's calculate how much she had left after spending 1/3 of her money:
2/3 * x = (2x/3)
Now, Julia lost 1/2 of the remaining money, so she has 1/2 * (2x/3).
According to the problem, she now has $10 remaining. So we can set up the equation:
1/2 * (2x/3) = 10
Simplifying the equation:
x/3 = 10
Multiplying both sides of the equation by 3:
x = 30
Therefore, Julia had $30 before spending 1/3 of her money.
To calculate how much Julia got for her birthday, we'll need to work backward.
Let's assume Julia's initial amount of money was represented by 'x'.
According to the information given:
- Julia spent 1/3 of her money, which means she had (x - 1/3x) = 2/3x remaining.
- Then she lost 1/2 of the remaining money, leaving her with (2/3x - 1/2(2/3x)) = 10 dollars.
Now, we can solve for 'x':
2/3x - (2/3)(1/2)x = 10
2/3x - 1/3x = 10
(2/3 - 1/3)x = 10
(1/3)x = 10
x = 10 * 3
x = 30
Therefore, Julia initially had $30. So, the amount she got for her birthday was $30.