The larger of two numbers is 11 more than twice the smaller number the sum of the numbers is 44 find each number

y = 11 + 2 x

x+y = 44 so x = 44 - y

y = 11 + 2 (44-y)
y = 11 + 88 - 2 y
3 y = 99
etc

Smaller number = X.

Larger number = 2x + 11.
x + (2x+11) = 44.
X = 11.
2x + 11 = 2*11 + 11 = 33.

Let's assume the smaller number as 'x'.

According to the given information, the larger number is 11 more than twice the smaller number. Therefore, the larger number can be represented as 2x + 11.

The sum of the numbers is given as 44. So, we can write an equation:

x + (2x + 11) = 44

Now, let's solve this equation step-by-step to find the value of 'x':

x + 2x + 11 = 44 (combine like terms)
3x + 11 = 44 (combine like terms)

To isolate 'x', subtract 11 from both sides of the equation:

3x + 11 - 11 = 44 - 11
3x = 33

Divide both sides of the equation by 3 to solve for 'x':

3x/3 = 33/3
x = 11

So, the smaller number is 11.

To find the larger number, we substitute the value of 'x' into our equation:

2x + 11 = 2 * 11 + 11
2x + 11 = 22 + 11
2x + 11 = 33

Therefore, the larger number is 33.

In conclusion, the smaller number is 11 and the larger number is 33.

To find the two numbers, let's represent them as variables. Let's say the smaller number is "x" and the larger number is "y".

Given that the larger number is 11 more than twice the smaller number, we can write the equation:

y = 2x + 11 ---(Equation 1)

We are also given that the sum of the numbers is 44, so we can write another equation:

x + y = 44 ---(Equation 2)

Now, we have a system of two equations with two variables. We can solve this system of equations using the substitution or elimination method:

Let's use the substitution method to solve the system:

Step 1: Solve Equation 1 for y:

y = 2x + 11

Step 2: Substitute the expression for y in Equation 2:

x + (2x + 11) = 44

Step 3: Simplify and solve for x:

3x + 11 = 44
3x = 33
x = 11

Step 4: Now substitute the value of x back into Equation 1 to find y:

y = 2x + 11
y = 2(11) + 11
y = 22 + 11
y = 33

Therefore, the smaller number (x) is 11 and the larger number (y) is 33.