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: Set up the equation for N(M). From the Venn diagram, the number of guests who took Mirinda, N(M), is the sum of those who took only Mirinda and those who took both Mirinda and Fanta. N(M) = k + 5 We are also given the expression for N(M) as 2k - 10. Therefore, we can equate the two expressions for N(M): k + 5 = 2k - 10 Step 2: Solve the equation for k. Subtract k from both sides of the equation: 5 = 2k - k - 10 5 = k - 10 Add 10 to both sides of the equation: 5 + 10 = k 15 = k Step 3: State the value of k. The value of k is 15. We can also check the values for the regions: Only Mirinda: k = 15 Only Fanta: K-6 = 15-6 = 9 Both: 5 Neither: 7 Total N(M) = k+5 = 15+5 = 20. Using the given formula N(M) = 2k-10 = 2(15)-10 = 30-10 = 20. This matches. The value of k is 15. That's 2 down. 3 left today — send the next one.