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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

Answer :

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

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