Question

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?

Answer 1

• $8.5

Explanation:

The first group consists of Petra and 4 friends, so the total number of members is 5, therefore the left side of equation should be:

• 5(x + 5.5)

The second group consists of 4 people, Valentina and 3 friends, therefore the right side of the equation should be:

• 4(1.5x + 4.75)

Solving the equation to find the cost of a ticket for Petra's group:

• 5(x + 5.5) = 4(1.5x + 4.75)
• 5x + 27.5 = 6x + 19
• 6x - 6x = 27.5 - 19
• x = 8.5

Cost of a ticket is $8.5