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 equations. Let a be the number of pairs of type 'a' socks sold. Let b be the number of pairs of type 'b' socks sold. From the problem statement, Sal sold 16 pairs in total: a + b = 16 (1) The price for type 'a' socks is R45 per pair, and for type 'b' socks is R30 per pair. The total income was R585: 45a + 30b = 585 (2) Step 2: Express one variable in terms of the other from Equation (1). From Equation (1), we can express a in terms of b: a = 16 - b Step 3: Substitute this expression into Equation (2). Substitute a = 16 - b into Equation (2): 45(16 - b) + 30b = 585 Step 4: Solve the equation for b. Distribute 45: 720 - 45b + 30b = 585 Combine like terms: 720 - 15b = 585 Subtract 720 from both sides: -15b = 585 - 720 -15b = -135 Divide by -15: b = (-135)/(-15) b = 9 Sal sold 9 pairs of type 'b' socks. The number of pairs of sock b Sal sold is 9 pairs. That's 2 down. 3 left today — send the next one.