Question: Honors Only Section: Use the following receipts and create a system of equations and then either…

Honors Only Section: Use the following receipts and create a system of equations and then either put both the equations into Desmos graphing calculator to find the solution to this system OR solve them using Elimination method. Write the solution below.

CINEMA SNACKSHAK Customer #7558 3 Large popcorn buckets 2 small drinks Total due: $21.00

CINEMA SNACKSHAK Customer #3555 2 Large popcorn buckets 4 small drinks Total due: $22.00

Solution

Step 1: Define variables Let \( x \) be the price of one large popcorn bucket and \( y \) be the price of one small drink. & Step 2: Set up the system of equations \[ \begin{cases} 2x + 2y = 13.96 & \\ 2x + 4y = 15.73 & \end{cases} \] Step 3: Subtract the first equation from the second \[ 2y = 1.77 \] Step 4: Solve for \( y \) \[ y = 0.885 \] Step 5: Substitute \( y \) back into the first equation \[ 2x + 2(0.885) = 13.96 \] \[ 2x + 1.77 = 13.96 \] \[ 2x = 12.19 \] \[ x = 6.095 \] Therefore, the price of one large popcorn bucket is \$6.095 and one small drink is \$0.885.