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
here are the solutions to the questions: b) Solve the following simultaneous equations: (3)/(4)p + 2q = 3 (1) p + 2q = 6 (2) Step 1: From equation (2), express 2q in terms of p. 2q = 6 - p (3) Step 2: Substitute equation (3) into equation (1). (3)/(4)p + (6 - p) = 3 Step 3: Solve for p. (3)/(4)p + 6 - p = 3 6 - 3 = p - (3)/(4)p 3 = (4)/(4)p - (3)/(4)p 3 = (1)/(4)p p = 3 × 4 p = 12 Step 4: Substitute the value of p back into equation (3) to find q. 2q = 6 - 12 2q = -6 q = (-6)/(2) q = -3 The solution is p = 12 and q = -3. c) Adama and Janita shared X cups of rice in the ratio 2:3. If Janita's share is 270 cups, find the value of X. Step 1: Determine the total number of ratio parts. The ratio for Adama : Janita is 2 : 3. Total parts = 2 + 3 = 5 parts. Step 2: Determine the fraction of the total share that Janita received. Janita's share corresponds to 3 parts out of 5 total parts, so Janita received (3)/(5) of the total rice. Step 3: Set up an equation using Janita's share and solve for X. (3)/(5) × X = 270 X = 270 × (5)/(3) X = 90 × 5 X = 450 The value of X is 450 cups. What's next?