Raj spends 2/3 of his money on a bike. Then he buys a helmet for $45. He uses 50% of the remaining money for shin guards. He has $2.50 left.How much was the bike?

You need to start with your ending amount, which is $2.50 and you purchased shin guards with 50% of your cash to arrive at $2.50 so take your $2.50 times 2. Next add $45 to get an answer. Now take your answer and times it by 3 and that is your final answer.