Jack had less than $20 saved and needed a lot more to buy a bicycle. His father agreed to add an amount equal to half whatever Jack had in his total savings whenever Jack received a grade of 90 or above on a math test. In this way, with his father's additional amounts, Jack's savings increased to exactly $81. With how much money did Jack begin?

Question

Jack had less than $20 saved and needed a lot more to buy a bicycle. His father agreed to add an amount equal to half whatever Jack had in his total savings whenever Jack received a grade of 90 or above on a math test. In this way, with his father's additional amounts, Jack's savings increased to exactly $81. With how much money did Jack begin?

Answer 1

Let X be the amount Jack originally had.

His father added (1/2)X for each math test with a grade of 90 or above.
Jack's new total would be X + (1/2)X = (3/2)X
He now has $81: (3/2)X = 81
So, X = 81 * (2/3) = 54.

Jack originally had $54 saved.