The sum of three numbers is 24 . The third is 7 more than 6 times the second. 4 times the first is 6 more than 2 times the second. Find the numbers. Shiow your work here

Step 1 ：Let's denote the three numbers as \(x\), \(y\), and \(z\).

Step 2 ：From the problem, we can form three equations:

Step 3 ：\(x + y + z = 24\) (The sum of three numbers is 24)

Step 4 ：\(z = 6y + 7\) (The third is 7 more than 6 times the second)

Step 5 ：\(4x = 2y + 6\) (4 times the first is 6 more than 2 times the second)

Step 6 ：Solving these equations, we get the solution: \(x = \frac{38}{15}\), \(y = \frac{31}{15}\), and \(z = \frac{97}{5}\)

Step 7 ：Final Answer: The three numbers are \(\boxed{\frac{38}{15}}\), \(\boxed{\frac{31}{15}}\), and \(\boxed{\frac{97}{5}}\)