I NEED HELP BADLY

Question

At the movies, Devin bought three tickets, one drink, and one bag of popcorn for $43.75.

Neil bought one ticket, three drinks, and two bags of popcorn for $27.75

Jung bought two tickets, two drinks, and one bag of popcorn for $34.

Determine the values that replace the letters in the augmented matrix which represents the situation. then Use the completed augmented matrix to find out the prices for one ticket, one drink, and one bag of popcorn.

Answer 1

I'll start by helping you put the problem into matrix form, but then I'll leave it to you to see if you can reduce the matrix to finish solving. Feel free to post a comment if you get stuck.

OK, let's use t for tickets, d for drinks, and p for popcorn. Sometimes it's easier to see what's going on if we start with the system of equations and then put it in a matrix, so that's what I'll do here.

Devin: 3 tickets, 1 drink, 1 popcorn, $43.75 dollars -> in equation form, that's 3t + 1d + 1p = 43.75

Neil: 1 ticket, 3 drinks, 2 popcorns, $27.75 dollars -> 1t + 3d+ 2p = 27.75

Jung: 2 tickets, 2 drinks, 1 popcorn, $34 -> 2t + 2d + 1p = 34

Now, we have 3 equations with 3 variables (often called unknowns). Putting this into a matrix form (you'll have to forgive the format, it's difficult to get the square brackets to go all the way to the bottom, and in an augmented matrix, you should show a vertical line separating the last column from the rest of the matrix)

[3 1 1 43.75

1 3 2 27.75

2 2 1 34 ]

Now that we have the problem in matrix form, you're left to reduce it and solve for the 3 unknown variables (the cost of a ticket, a drink, and a bag of popcorn).

I hope this helps! Let me know if you're still stuck, and we'll try to take it a bit further.

Answer 2

At the movies, Devin bought three tickets, one drink, and one bag of popcorn for $43.75.

Neil bought one ticket, three drinks, and two bags of popcorn for $27.75

Jung bought two tickets, two drinks, and one bag of popcorn for $34.

Determine the values that replace the letters in the augmented matrix which represents the situation. then Use the completed augmented matrix to find out the prices for one ticket, one drink, and one bag of popcorn.

...Let...

T represents Tickets

D represent Drink

P represent Popcorn

....Now express each situation from word problem as math equations....

At the movies, Devin bought three tickets, one drink, and one bag of popcorn for $43.75.

3T + 1D + 1P = $43.75

Neil bought one ticket, three drinks, and two bags of popcorn for $27.75

1T + 3D + 2P = $27.75

Jung bought two tickets, two drinks, and one bag of popcorn for $34.

2T + 2D + 1P = $34

....You now have a common 3 equations and 3 unknowns problem......

Place this information into your matrix to complete the solution steps....What do you think?