Penny has bought a scarf for $5.00, spent 1/2 of her remaining money on jogging shoes, bought lunch for $2.00, then spent 1/2 of her remaining money on a present. She had $10 left. How much did she start with?

So you work backwards. You start with 10, and that was half her money so she had 20 dollars prior to buying the gift. Then she bought lunch so now it is 22 dollars. Again that is half of what she had prior to buying the shoes so she had 44 dollars before she bought the shoes. She bought a scarf for 5 dollars so add that to 44 and you get 49 Dollars. Penny started with 49 Dollars.