A student wrote the equation 4(x+5.5)=3(1.5x+4.75) to represent the problem shown. Find her mistake and correct it.

Petra and her 4 friends went to the movies. They each bought a ticket for x dollars and spent $5.50 each on snacks. Valentina and her 3 friends went to the movies and paid 1.5 times as much for each of their tickets as Petra. Everyone in Valentina’s group also spent $4.75 each on snacks. If both groups spent the same amount, what is the cost of a ticket for Petra’s group?