Question

You are in charge of a concession stand for a game at your school. The note from your teacher advisor is a little hard to read, but you think it says “Sell a hot dog and chips for $3, or sell four hot dogs and four bags of chips for $10.” The note didn’t say how much to sell an individual hot dog or an individual bag of chips for, so you need to figure that out.
Journal Entry #1:
Write a system of equations to represent this situation, and solve the system to find out how much each individual hot dog or bag of chips should cost. Did you have any problem solving it? If so, what was the problem, and what does it mean? Show all of your work.
Journal Entry #2:
You call your teacher and find out that the second part of the note should have said “sell four hot dogs and two bags of chips for $10.” What does that do for your system of equations now? With this new information, how much should each item cost? Again, show all of your work.

Answer 1

The new information implies that the number of hot dogs is 1 and the bags of chips is 2

The system of equations

The statements are given as:

“Sell a hot dog and chips for $3, or sell four hot dogs and four bags of chips for $10.

Represent the hot dog with x and the chips with y.

So, we have

x + y = 3

4x + 4y = 10

How to solve the system of equations

In (a), we have:

x + y = 3

4x + 4y = 10

Multiply the first equation by 4

4x + 4y = 12

Subtract this equation from the second equation

4x - 4x + 4y - 4y = 12 - 10

Evaluate

0 = 2

The above equation is false.

This means that the system of equations has no solution

What does that do for your system of equations now?

The second statement is given as:

"sell four hot dogs and two bags of chips for $10.”

So, we have the following system of equations:

x + y = 3

4x + 2y = 10

Make x the subject in x + y = 3

x = 3 - y

Substitute x = 3 - y in 4x + 2y = 10

4(3 - y) + 2y = 10

Expand the bracket

12 - 4y + 2y = 10

Evaluate the like terms

2y = 2

Divide by 2

y = 1

Substitute y = 1 in x = 3 - y

x = 3 - 1

Evaluate

x = 2

Hence, the new information implies that the number of hot dogs is 1 and the bags of chips is 2

Read more about system of equations at:

brainly.com/question/13729904

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