The sum of two numbers is 47. the larger number is 11 more than the smaller number. what are the numbers?

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!