Question

Alicia and Neha 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 X be the amount Neha had at first.
After Alicia spent 1 3 of her money, she had X - X/3 = 2/3*X left.
After Neha spent $10, she had X - $10 left.
2/3*X = 1/2*(X - $10)
2/3*X = 1/2*X - 1/2*$10
2/3*X - 1/2*X = - 1/2*$10
4/6*X - 3/6*X = -1/2*$10
X/6 = -$10/2
X/6 = -$5
X = -$5 * 6
X = -$30
Neha had -$30 at first. Answer: \boxed{30}.