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?

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Each bought one ticket and spent $4.75 on snacks. There were four in the group (Valentina and three friends). Their tickets were 1.5 times the price of Petra's group, so 1.5x is the cost of each ticket. Total expenses:

4(1.5x+4.75)

We learn both spent the same amount, so set them equal to each other:

5(x+5.50) = 4(1.5x+4.75)

The student's mistake was in the number of people in each group. She had

4 in Petra's group (should be 5) and 3 in Valentina's group (should be 4)

Using the correct equation:

5(x+5.50) = 4(1.5x+4.75)

5x+27.50 = 6x+19.00

-x = -8.50

x = $8.50 Price of a ticket for Petra's group.

1.5x = $12.75 Price of a ticket for Valentino's group.

Check to see if both groups did indeed pay the same total amounts:

Tickets Snacks Total

Petra: (5*8.50) = 42.50 (5*5.50) = 27.50 $70.00

Valentino: (4*12.75) = 51.00 (4*4.75) = 19.00 $70.00