This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Define variables and set up the system of equations. Let a be the number of pairs of sock type a. Let b be the number of pairs of sock type b. From the problem statement, we have two pieces of information: 1. Total number of pairs sold: a + b = 16 (1) 2. Total income from sales: 45a + 30b = 585 (2) Step 2: Solve equation (1) for a in terms of b. a = 16 - b Step 3: Substitute this expression for a into equation (2). 45(16 - b) + 30b = 585 Step 4: Distribute and simplify the equation. 45 × 16 - 45b + 30b = 585 720 - 45b + 30b = 585 720 - 15b = 585 Step 5: Isolate the term with b. -15b = 585 - 720 -15b = -135 Step 6: Solve for b. b = (-135)/(-15) b = 9 Sal sold 9 pairs of sock type b. Step 7: (Optional) Find a to verify the total number of pairs and income. a = 16 - b = 16 - 9 = 7 Check total income: 45(7) + 30(9) = 315 + 270 = 585. This matches the given total income. The number of pairs of sock b Sal sold is: 9 Last free one today — make it count tomorrow, or type /upgrade for unlimited.