miaespinoza300
Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Marie, Shelia, and Martha bought snacks for a girl's sleepover. They each bought the items shown in the following table at the local convenience store:
Number of bags of chips, Number of liters of pops, Number of chocolate bars, Cost
2 2 1 $9.25
3 4 1 $14.50
1 3 3 $12.00

Calculate the unit price of each snack purchased by the girls

Sagot :

Using a system of equations, it is found that the unit prices are:

  • $2.25 for a bag of chips.
  • $1.50 for a liter of pop.
  • $1.75 for a chocolate bar.

For the system:

  • x is the unit price of a bag of chips.
  • y is the unit price of liter of pop.
  • z is the unit price for a chocolate bar.

From the table, the equations are:

[tex]2x + 2y + z = 9.25[/tex]

[tex]3x + 4y + z = 14.50[/tex]

[tex]x + 3y + 3z = 12[/tex]

Replacing the first equation on the second and the third:

[tex]z = 9.25 - 2x - 2y[/tex]

[tex]3x + 4y + z = 14.50[/tex]

[tex]3x + 4y + 9.25 - 2x - 2y = 14.50[/tex]

[tex]x + 2y = 5.25[/tex]

[tex]x = 5.25 - 2y[/tex]

[tex]x + 3y + 3z = 12[/tex]

[tex]x + 3y + 3(9.25 - 2x - 2y) = 12[/tex]

[tex]-5x - 3y = -15.75[/tex]

[tex]5x + 3y = 15.75[/tex]

Since [tex]x = 5.25 - 2y[/tex]:

[tex]5(5.25 - 2y) + 3y = 15.75[/tex]

[tex]-7y = -10.5[/tex]

[tex]y = \frac{10.5}{7}[/tex]

[tex]y = 1.5[/tex]

Then:

[tex]x = 5.25 - 2y = 5.25 - 2(1.5) = 2.25[/tex]

[tex]z = 9.25 - 2x - 2y = 9.25 - 2(2.25) - 2(1.5) = 1.75[/tex]

The unit prices are:

  • $2.25 for a bag of chips.
  • $1.50 for a liter of pop.
  • $1.75 for a chocolate bar.

A similar problem, also solved using a system of equations, is given at https://brainly.com/question/14183076

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.