Question

the sum of two numbers is 60. the larger number is 18 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 $x + 18$.

Step2: Set up equation

The sum of the two numbers is 60, so we have the equation $x+(x + 18)=60$.

Step3: Solve the equation

Simplify the left - hand side: $2x+18 = 60$.
Subtract 18 from both sides: $2x=60 - 18=42$.
Divide both sides by 2: $x=\frac{42}{2}=21$.

Step4: Find the larger number

The larger number is $x + 18=21+18 = 39$.

Answer:

Larger number: 39
Smaller number: 21