Grace had a total of $$2540$$ pins and needles at first. After she sold $$1820$$ pins and $$\frac{4}{5}$$ of the needles, she had an equal number of pins and needles left. How many needles did Grace have left?~\uline{~~~~~~~~~~}~needles.     Paul\textquotesingle s workings are as below:  Since $$1820$$ pins is equivalent to $$\frac{4}{5}$$ of the needles,  $$4u=1820$$  $$1u=1820\div4=455$$  She had $$455$$ needles left.     Is Paul\textquotesingle s solution correct? If not, find the correct answer, draw a model and show all your workings. 
Overseas Competition->Knowledge Point->Counting Modules