Solving System of Equations Word Problems: Apples and Bananas

Setting Up the Equations

• 🍎 Lauren's purchase is represented by the equation 8A + 9B = $9.25, where A is the price of an apple and B is the price of a banana.
• 🍌 Andrew's purchase is represented by the equation 7A + 6B = $7.25.

Solving for the Unit Price of an Apple

• 🎯 To solve for the price of an apple (A), we aim to eliminate the variable B.
• ✖️ Multiply Lauren's equation by 2 and Andrew's equation by -3 to get a common multiple for B (18).
• ➖ This results in -5A = -3.25, leading to an apple price (A) of $0.65.

Solving for the Unit Price of a Banana

• ➕ Substitute the price of an apple ($0.65) back into Lauren's original equation (8A + 9B = $9.25).
• ➖ This gives 8($0.65) + 9B = $9.25, simplifying to $5.20 + 9B = $9.25.
• ➗ Subtracting $5.20 from both sides yields 9B = $4.05, resulting in a banana price (B) of $0.45.

Calculating the Final Cost

• 🛒 The problem asks for the cost of nine apples and seven bananas (9A + 7B).
• 💰 Using the calculated prices, 9($0.65) + 7($0.45) equals $5.85 + $3.15.
• ✅ The total cost for Aaron to buy nine apples and seven bananas is $9.00.