Mark-up, discounts and a profit target

A shopkeeper buys a jacket for \(\$C\) and marks its price \(40\%\) above the cost price.

1. Find her percentage profit if she sells the jacket at a \(15\%\) discount on the marked price.[2]
2. Find the largest percentage discount she can give if she wants a profit of at least \(5\%\) of the cost price.[3]
3. In a sale she takes \(20\%\) off the marked price and then a further \(10\%\) off the reduced price. A customer says this is a \(30\%\) discount. Explain whether the customer is right, and whether the shopkeeper still makes at least \(5\%\) profit.[2]