Question

Caroline was thinking of a number. Caroline adds 7 to it, then doubles it and gets an answer of 82.8. What was the original number?

Answer 1

n = 34.4

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

Explanation:

Step 1: Set Up

Let's let our number be set by variable n.

We add 7 to it: n + 7

We then double that entire expression: 2(n + 7)

That expression is equal to 82.8: 2(n + 7) = 82.8

Step 2: Solve for n

1. [Division Property of Equality] Divide 2 on both sides: n + 7 = 41.4
2. [Subtraction Property of Equality] Subtract 7 on both sides: n = 34.4

∴ Caroline's original number is 34.4.