priscillazhagui22
Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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?

!!!​

Sagot :

rspill6

Answer:

A ticket for Petra's group is $8.50

Step-by-step explanation:

Petra's Group

Each bought one ticket and spent $5.50 on snacks.  There were five in the group (Petra and four friends).  Total expenses:

5(x+5.50)

Valentina's Group

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

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.