Let's break down the information in the problem:

• Kehlani bought:

  • 6 bags of popcorn
  • 8 drinks
  • Total cost: $76

• Madelyn bought:

  • 7 bags of popcorn
  • 4 drinks
  • Total cost: $62

We need to find the price of each bag of popcorn (let's call it $x$) and the price of each drink (let's call it $y$).

System of Equations

From the given information, we can set up two equations based on the costs:

1. For Kehlani: $6x + 8y = 76$

2. For Madelyn: $7x + 4y = 62$

Solving the System of Equations

We can use substitution or elimination to solve this system of equations. Let's use the elimination method by eliminating one of the variables.

1. Multiply the first equation by 2 to make the coefficients of $y$ the same in both equations: $12x + 16y = 152$

2. Subtract the second equation from this new equation: $(12x + 16y) - (7x + 4y) = 152 - 62$ Simplifying: $5x + 12y = 90$

Now subtracting: [ 5x = 90 - 79 ×