You and your friend are buying throw blankets with your names embroidered on them. The cost of the throw blanket is $x$ dollars and the cost of each embroidered letter is $y$ dollars. Your name has $6$ letters and the total cost is $$29.$ Your friend's name has $3$ letters and the total cost is $$24\mathrm{.}50.$ Find the cost of the throw blanket and the cost of each embroidered letter.