Mike and Paul went shopping together with a total sum of $90. Mike spent twice as much as Paul. The amount Paul had left was $9 more than what he had spent. He had twice as much money left as Mike.

Question

(a) How much money did Paul spend?
(b) How much money did Mike have at first?

Answer 1

Let's assume that Paul spent x dollars.

According to the question, Mike spent twice as much as Paul, so Mike spent 2x dollars.

The amount of money Paul had left was $9 more than what he had spent, so Paul had x + $9 dollars left.

He had twice as much money left as Mike, so x + $9 = 2(2x) = 4x.
=> 4x = x + $9
=> 4x - x = $9
=> 3x = $9
=> x = $9/3 = $3

Therefore, Paul spent $3.

To find out how much money Mike had at first, we need to add the money he spent to the money he had left.
Mike had 2x = 2 * $3 = $6 left.
So, he spent $90 - $6 = $84.

Therefore, Mike had $84 at first. Answer: \boxed{84}.