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.
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Final Answer: The three numbers are $\frac{38}{15}$ , $\frac{31}{15}$ , and $\frac{97}{5}$

Steps

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

Step 5 ： $4 x = 2 y + 6$ (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 $\frac{38}{15}$ , $\frac{31}{15}$ , and $\frac{97}{5}$