Answer:
The numbers described here are 39 and 11.
Explanation:
Let's call the numbers a and b, a being the larger. We're told two things:
The larger of the two numbers is 17 more than twice the smaller.
Which we can express as:
a = 2b + 17
When the larger number is divided by the smaller, the quotient is 3 and the remainder is 6
And that can be expressed as:
a = 3b + 6
We can now take those two expressions and, noting that they both define a, we can say that they are equivalent, and solve for b:
2b + 17 = 3b + 6
3b - 2b = 17 - 6
b = 11
With b found, we can now take either of the first expressions, and solve for a:
a = 2b + 17
a = 2(11) + 17
a = 22 + 17
a = 39
Now we can check whether that is correct by plugging it into the other expression and seeing if b still comes to 11:
a = 3b + 6
39 = 3b + 6
3b = 33
b = 11
So we know that the answer is correct.