To solve for this, we need to translate our system of equations into parenthesis.
The sum of two numbers (x + y) is (=) 47 (47). The larger number (x) is (=) 11 more (+11) than the smaller number (y).
Let's rewrite each sentence but only with the parenthesis.
x + y = 47.
x = y + 11.
This is our system of equations, and will help us solve for x and y.
Given that x is y + 11, we can safely assume x is a larger number, giving the higher portion of the sum between the two numbers.
y must be a smaller number, and most likely is less than half of 47.
We can also assume that both our numbers' must sum up to a number that ends in 7 in the ones place.
We must also know that since x-11 = y, both the numbers in the ones place must make a difference of 1, since 11 has a 1 in the ones place.
Let's make a list of numbers that have sum of 7 in the ones place and a difference of 1 in the ones place.
4 - 3 = 1
4 + 3 = 7
9 + 8 = 17
9 -8 = 1
These are our only 4 numbers that have a sum of 7/17 and a difference of 1.
Since y + 11 = x, let's try a number ~20's for x and a number ~10's for y.
29 = x
18 = y
29 + 18 = 47. (x + y = 47)
29 - 18 = 11. (x = y + 11)
Your final numbers are 29 and 18.
I hope this helps!