Question

The sum of two numbers is 67. The difference of the two numbers is 53. What are the two numbers?

Answer 1

One number is 60 and the other is 7.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients
• Solving systems of equation using substitution/elimination

Explanation:

Step 1: Define

Identify and set up

Let x be one number and y be the other.

x + y = 67

x - y = 53

Step 2: Solve for x

Elimination

1. Combine two equations: 2x = 120
2. [Division Property of Equality] Divide 2 on both sides: x = 60

Step 3: Solve for y

1. Substitute in x [1st Equation]: 60 + y = 67
2. [Subtraction Property of Equality] Subtract 50 on both sides: y = 7