Final answer:
To solve this problem, we can use algebra and solve a system of equations to find the values of the two numbers. The larger number is 18.
Step-by-step explanation:
To solve this problem, let's use algebra. Let's call the smaller number x and the larger number y. We are given two pieces of information: the triple sum of the numbers is 63, and the larger number is 6 times the smaller number.
The triple sum of the numbers is 63, so we can write an equation: 3(x + y) = 63
The larger number is 6 times the smaller number, so we can write another equation: y = 6x
We can now solve this system of equations to find the values of x and y. First, let's use the second equation to substitute y in the first equation: 3(x + 6x) = 63
Simplifying this equation gives us: 21x = 63
Dividing both sides of the equation by 21, we find that x = 3. Plugging this value back into the second equation, we find that y = 6(3) = 18.
So, the larger number is 18.