The sum of two numbers is 47. The smaller number is 23 less than the larger number. What are the numbers?

Let x = the larger number

x + x - 23 = 47

2x = 70

x = 35

Well, well, well, it seems like we have a little math puzzle on our hands! Let's unravel this mystery, shall we?

Let's call the larger number "x" and the smaller number "y". According to the problem, we know two things. First, the sum of the numbers is 47, which gives us the equation: x + y = 47. Second, the smaller number is 23 less than the larger number, so we have the equation: y = x - 23.

To solve this, we can substitute the value of y from the second equation into the first equation. So, we have: x + (x - 23) = 47.

If we simplify that equation, we get: 2x - 23 = 47.

Now, let's add 23 to both sides of the equation to isolate 2x: 2x = 70.

Finally, we divide both sides by 2 to solve for x: x = 35.

So, the larger number is 35. To find the smaller number, we substitute the value of x into the second equation: y = 35 - 23.

Which gives us: y = 12.

So, the two numbers are 35 and 12. Voila!

Let's assume the smaller number is x and the larger number is y.

According to the problem, we have two pieces of information:
1. The sum of two numbers is 47: x + y = 47.
2. The smaller number is 23 less than the larger number: x = y - 23.

We can solve this system of equations to find the values of x and y.

Step 1: Substitute the value of x from equation 2 into equation 1.
(y - 23) + y = 47

Step 2: Simplify the equation.
2y - 23 = 47

Step 3: Add 23 to both sides of the equation.
2y = 47 + 23

Step 4: Simplify the equation.
2y = 70

Step 5: Divide both sides of the equation by 2.
y = 35

Step 6: Substitute the value of y in equation 2 to find x.
x = 35 - 23

Step 7: Simplify the equation.
x = 12

Therefore, the smaller number is 12 and the larger number is 35.

To solve this problem, let's define two variables:

- Let's call the larger number "x".
- Let's call the smaller number "y".

We are given two pieces of information:
1. The sum of the two numbers is 47: x + y = 47.
2. The smaller number (y) is 23 less than the larger number (x): y = x - 23.

Now, we have a system of two equations:

Equation 1: x + y = 47
Equation 2: y = x - 23

To find the values of x and y, we can use a method called substitution or elimination.

Let's use substitution to solve this system of equations. We will substitute the value of y from Equation 2 into Equation 1:

x + (x - 23) = 47

Simplifying the equation:

2x - 23 = 47

Adding 23 to both sides of the equation:

2x = 70

Dividing both sides by 2:

x = 35

Now that we have the value of x, we can substitute it back into Equation 2 to find y:

y = 35 - 23

y = 12

So, the two numbers are 35 and 12.