Answer to hard math question

Question

Paul and Ian had a total of $63. After Paul gave 0.3 of his money to Ian, Ian gave ⅓ of his total amount of money too Calvin. If all three boys have the same amount in the end, how much did Paul have at first?

Answer 1

There is a total of $63 between all three people. So they have to have $63/3 in the end or $21. If Paul have 30% (0.3) of his money to Ian, then he is left with 70% of his initial money. If he ends up with $21, then

0.7(P_I) = 21

21/0.7 = 30

Paul started with $30

Answer 2

Let P be initial amount Paul had

Let I be initial amount Ian had

P + I = 63

P = 63 - I

After giving 0.3 of Paul's money to Ian

Paul has 0.7 P

Ian has I + 0.3 P

They have the same amount of money

0.7 P = I + 0.3 P

0.7 (63 - I) = I + 0.3 (63 - I)

I = 18

P = 45 (Paul had $45 at first)

We don't really need 1/3 of Ian's total money that was given to Calvin to calculate Paul's initial amount, unless the question also asked Calvin's money.