Question

Samira and Morgan went shopping for a class party. Samira bought 8 two-liters of drinks and 4 bags of chips for a total of $20. Morgan bought 6 two-liters and 10 bags of chips for a total of $29. How much did they spend on each two-liter and each bag of chips?

A) $1.75 per two-liter and $2 per bag of chips
B) $2 per two-liter and $1.50 per bag of chips
C) $1.50 per two-liter and $2 per bag of chips
D) $2 per two-liter and $2.50 per bag of chips

Answer 1

By setting up a system of equations and using elimination, we find that the two-liters are priced at $1.50 each, and bags of chips are priced at $2 each. The correct answer is C) $1.50 per two-liter and $2 per bag of chips.

Step-by-step explanation:

To solve for the price of each two-liter of drink and each bag of chips that Samira and Morgan bought, we can set up a system of equations based on the information given. Let's denote the price of a two-liter as x and the price of a bag of chips as y.

Samira's purchase can be represented by the equation:
8x + 4y = 20

Morgan's purchase can be represented by the equation:
6x + 10y = 29

To solve the system, we can use the method of substitution or elimination. For this example, we'll use elimination.

• Multiply the first equation by 2.5 to align the y-coefficients:
  20x + 10y = 50
• Now subtract the second equation from this new equation:
  20x + 10y - (6x + 10y) = 50 - 29
  14x = 21
  x = 21 / 14
  x = $1.50 per two-liter
• Substitute the value of x into one of the original equations:
  6(1.50) + 10y = 29
  9 + 10y = 29
  10y = 20
  y = 20 / 10
  y = $2 per bag of chips

Therefore, the correct answer is the two-liter of drink is $1.50 each, and each bag of chips is $2.