The cost of 5 notebooks and 3 pens is $23. The cost of 3 notebooks and 2 pens is $14. What is the cost of one notebook?
["Understanding the Cost Breakdown: Solving for the Price of One Notebook", "If you've ever shopped for school supplies, you may have encountered a classic math-based pricing puzzle — like knowing the combined cost of notebooks and pens helps uncover each item’s price. Today, we break down a simple yet effective system of equations to determine the cost of one notebook, based on two budget-friendly purchase scenarios.", "---", "### The Problem at Hand", "We’re given:", "- The cost of 5 notebooks and 3 pens is $23.\n- The cost of 3 notebooks and 2 pens is $14.", "We want to find:\nThe price of one notebook.", "---", "### Step 1: Set Up the Equations", "Let:\n- $ n $ = cost of one notebook (in dollars)\n- $ p $ = cost of one pen (in dollars)", "From the problem, we form two equations:", "1. $ 5n + 3p = 23 $\n2. $ 3n + 2p = 14 $", "---", "### Step 2: Eliminate One Variable", "We’ll eliminate $ p $ to solve for $ n $.\nMultiply equation (1) by 2 and equation (2) by 3:", "- $ 2(5n + 3p) = 2 \ imes 23 $ → $ 10n + 6p = 46 $\n- $ 3(3n + 2p) = 3 \ imes 14 $ → $ 9n + 6p = 42 $", "Now subtract the second from the first:", "$$\n(10n + 6p) - (9n + 6p) = 46 - 42\n\Rightarrow n = 4\n$$", "---", "### Step 3: Find the Pen’s Price (Optional)", "To verify: Plug $ n = 4 $ back into one of the original equations:", "Using $ 3n + 2p = 14 $:\n$ 3(4) + 2p = 14 $\n$ 12 + 2p = 14 $\n$ 2p = 2 $\n$ p = 1 $", "So, a notebook costs $4 and a pen costs $1.", "---", "### Why This Matters (Solving Real-World Problems)", "Understanding how to set and solve systems of equations allows consumers and retailers alike to:", "- Accurately calculate costs based on bundle purchases\n- Identify pricing discrepancies\n- Make informed budgeting decisions", "---", "### Final Answer", "The cost of one notebook is $4.", "---", "Use this method next time your favorite notebook and pen grab a discount bundle — math helps you get the real value behind every item!", "Keywords: notebook cost, pen cost calculation, solve notebook price, math pricing problem, system of equations, supply store pricing, how to calculate notebook price"]
