Use the median information to form an equation.

Hey Hurry, good to see you again. Step 1: Use the median information to form an equation. The numbers 2, 9, 7m, 3n, 21, 24 are arranged in ascending order. There are 6 numbers. For an even set of numbers, the median is the average of the two middle terms. The 3rd term is 7m and the 4th term is 3n. The median is given as 16. (7m + 3n)/(2) = 16 Multiply both sides by 2: 7m + 3n = 32 (Equation 1) Step 2: Use the mean information to form a second equation. The numbers are 4, 8, 6, 4m, 19, 2n. There are 6 numbers. The mean is given as 9(1)/(2), which is (19)/(2) or 9.5. The mean is the sum of the numbers divided by the count of numbers. (4 + 8 + 6 + 4m + 19 + 2n)/(6) = 9.5 Sum the constant terms: 4 + 8 + 6 + 19 = 37. (37 + 4m + 2n)/(6) = 9.5 Multiply both sides by 6: 37 + 4m + 2n = 9.5 × 6 37 + 4m + 2n = 57 Subtract 37 from both sides: 4m + 2n = 57 - 37 4m + 2n = 20 Divide the entire equation by 2 to simplify: 2m + n = 10 (Equation 2) Step 3: Solve the system of linear equations. We have two equations: 1) 7m + 3n = 32 2) 2m + n = 10 From Equation 2, express n in terms of m: n = 10 - 2m Substitute this expression for n into Equation 1: 7m + 3(10 - 2m) = 32 7m + 30 - 6m = 32 m + 30 = 32 Subtract 30 from both sides: m = 32 - 30 m = 2 Step 4: Find the value of n. Substitute the value of m=2 back into the expression for n: n = 10 - 2(2) n = 10 - 4 n = 6 The values are m=2 and n=6. Step 5: Verify the solution. For the first set of numbers: 2, 9, 7m, 3n, 21, 24. Substitute m=2 and n=6: 2, 9, 7(2), 3(6), 21, 24 2, 9, 14, 18, 21, 24. The median is (14+18)/(2) = (32)/(2) = 16. This is correct. For the second set of numbers: 4, 8, 6, 4m, 19, 2n. Substitute m=2 and n=6: 4, 8, 6, 4(2), 19, 2(6) 4, 8, 6, 8, 19, 12. The sum is 4+8+6+8+19+12 = 57. The mean is (57)/(6) = 9.5 = 9(1)/(2). This is correct. The values are: m=2, n=6 Drop the next question!