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
