Question

The sum of two numbers is 37. Their difference is 11. What is the smaller number?

Answer 1

Hello from MrBillDoesMath!

Answer:

13

Discussion:

Let the numbers in the Question be call m and n. Then

m + n = 37

m - n = 11

Adding these 2 equations gives:

(m+ n) + (m - n) = 37 +11 =>

(m+m) + (n-n) = 48 =>

2m + 0 = 48 =>

m = 24.

As m + n = 37, 24 +n = 37 , so n = 13.

Thank you,

MrB

Answer 2

Step 1: Set up the equations

Let's denote the two numbers as x and y. From the problem, we know that:

- The sum of the two numbers is 37; thus, we have the equation x + y = 37
- The difference of the two numbers is 11; therefore, we have the equation x - y = 11

Step 2: Solving the equations

Now, we can proceed to solve these equations system.

If you add these two equations:
(x + y) + (x - y) = 37 + 11, you get:
2x = 48.

After you find that equation, it's obvious that you can find x by dividing both sides of it by 2 to solve for 'x', to get:
x = 48 / 2, and that gives:
x = 24.

Step 3: Finding the value of 'y'

Now that we have found the value of 'x', we can substitute it into the first equation (x + y = 37) to find 'y':
(24) + y = 37.
Solving for 'y', we get:
y = 37 - 24, and that gives:
y = 13.

Step 4: Determine the smaller number

Comparing 'x' and 'y', we can clearly see that 'y' with a value of 13 is smaller than 'x' with a value of 24. Therefore, the smaller number is 13.