Question

the sum of two numbers is 55. the larger number is 11 more than the smaller number. what are the numbers?
larger number:
smaller number:

Explanation:

Step1: Define variables

Let the smaller number be \( x \). Then the larger number is \( x + 11 \).

Step2: Set up equation

The sum of the two numbers is 55, so \( x+(x + 11)=55 \).

Step3: Solve the equation

Simplify the left side: \( 2x+11 = 55 \).
Subtract 11 from both sides: \( 2x=55 - 11=44 \).
Divide both sides by 2: \( x=\frac{44}{2}=22 \).

Step4: Find the larger number

The larger number is \( x + 11=22 + 11 = 33 \).

Answer:

Larger number: 33
Smaller number: 22