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
Okay, Samuel, let's adjust the problem with your new value for X. Step 1: Set up the equations with the given conditions. We assume the relationship is Y = C + kX, where C is the constant part and k is the constant of variation. Using the first condition: When X=3, Y=7. 7 = C + k(3) C + 3k = 7 (1) Using your new second condition: When X=4, Y=11. 11 = C + k(4) C + 4k = 11 (2) Step 2: Solve the system of linear equations for C and k. Subtract equation (1) from equation (2): (C + 4k) - (C + 3k) = 11 - 7 C + 4k - C - 3k = 4 k = 4 Step 3: Substitute the value of k back into one of the original equations to find C. Using equation (1): C + 3(4) = 7 C + 12 = 7 C = 7 - 12 C = -5 Step 4: State the constant of variation. The constant of variation is k. k = 4 The constant of variation is 4. That's 2 down. 3 left today — send the next one.