Before I answer your math question, I need to point out a couple of things about your question: the usual form for the $ sign is that the $ precedes the number, e.g. $25; the comma before the and is not necessary; and a question begins with a capital letter and ends with a ?. You no doubt expect my answer to be precise; likewise, I expect your question to be precise.
Let M = # of manicures and P = # of pedicures
M + P = 10
25M + 50P = 300 => M + 2P = 12
Subtract the first equation from the second: P = 2
then substitute in the first equation: M= 8