Alicia and nela had a total of $66. After Alicia spent 1 3 of her money and neha spent $10 the amount of money alicia had left was 1 2 of the amount of money neha had left. How much did neha have at first?

Answer 1

Let's say Alicia had x dollars.
After Alicia spent 1/3 of her money, she had x - (1/3)x = (2/3)x dollars left.
After Neha spent $10, Alicia had (2/3)x - 10 dollars left.
The amount of money Neha had left is 1/2 * ((2/3)x - 10).
Since Alicia and Neha had a total of $66, we can write the equation (2/3)x - 10 + 1/2 * ((2/3)x - 10) = 66.
Multiplying through the parentheses, we get (2/3)x - 10 + (1/2) * (2/3)x - (1/2)*10 = 66.
Multiplying further, we get (2/3)x - 10 + (1/3)x - 5 = 66.
Combining like terms, we get (5/3)x - 15 = 66.
Adding 15 to both sides, we get (5/3)x = 81.
Dividing both sides by (5/3), we get x = (3/5)*81 = <<(3/5)*81=48.6>>48.6 dollars.
Therefore, Neha had $48.6 at first. Answer: \boxed{48.6}.