1. **State the problem:** We have two equations representing the total cost of bags of popcorn and plates of nachos purchased by Jeremy and Kendrick: $$4p + 2n = 18.50$$ $$7p + 2n = 26.75$$ where $p$ is the cost per bag of popcorn and $n$ is the cost per plate of nachos. 2. **Goal:** Find the cost of one bag of popcorn ($p$) and one plate of nachos ($n$). 3. **Method:** Use the system of linear equations to solve for $p$ and $n$. 4. **Step 1: Subtract the first equation from the second to eliminate $n$:** $$ (7p + 2n) - (4p + 2n) = 26.75 - 18.50 $$ $$ 7p - 4p + 2n - 2n = 8.25 $$ $$ 3p = 8.25 $$ 5. **Step 2: Solve for $p$:** $$ p = \frac{8.25}{3} = 2.75 $$ So, one bag of popcorn costs 2.75. 6. **Step 3: Substitute $p = 2.75$ into the first equation to find $n$:** $$ 4(2.75) + 2n = 18.50 $$ $$ 11 + 2n = 18.50 $$ $$ 2n = 18.50 - 11 = 7.50 $$ 7. **Step 4: Solve for $n$:** $$ n = \frac{7.50}{2} = 3.75 $$ So, one plate of nachos costs 3.75. **Final answer:** A bag of popcorn costs 2.75 and a plate of nachos costs 3.75.