Question

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 1

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:

$2x + 2y + z = 9.25$

$3x + 4y + z = 14.50$

$x + 3y + 3z = 12$

Replacing the first equation on the second and the third:

$z = 9.25 - 2x - 2y$

$3x + 4y + z = 14.50$

$3x + 4y + 9.25 - 2x - 2y = 14.50$

$x + 2y = 5.25$

$x = 5.25 - 2y$

$x + 3y + 3z = 12$

$x + 3y + 3(9.25 - 2x - 2y) = 12$

$-5x - 3y = -15.75$

$5x + 3y = 15.75$

Since $x = 5.25 - 2y$:

$5(5.25 - 2y) + 3y = 15.75$

$-7y = -10.5$

$y = \frac{10.5}{7}$

$y = 1.5$

Then:

$x = 5.25 - 2y = 5.25 - 2(1.5) = 2.25$

$z = 9.25 - 2x - 2y = 9.25 - 2(2.25) - 2(1.5) = 1.75$

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 brainly.com/question/14183076