1/3 of a number decreased by 13 equals 45
The Correct Answer and Explanation is:
Answer:
Let the number be xxx.
According to the problem:13x−13=45\frac{1}{3}x – 13 = 4531x−13=45
Add 13 to both sides:13x=58\frac{1}{3}x = 5831x=58
Multiply both sides by 3:x=174x = 174x=174
Final Answer: 174\boxed{174}174
Explanation (Approximately 300 words):
To solve the equation “1/3 of a number decreased by 13 equals 45,” begin by translating the sentence into a mathematical equation. The phrase “1/3 of a number” indicates one-third of some unknown value, which is represented as 13x\frac{1}{3}x31x, where xxx is the unknown number. The term “decreased by 13” implies a subtraction of 13. Therefore, the expression becomes 13x−13\frac{1}{3}x – 1331x−13. The word “equals” suggests that this expression is set equal to 45. So the complete equation is:13x−13=45\frac{1}{3}x – 13 = 4531x−13=45
To isolate the variable xxx, follow a step-by-step process. First, eliminate the constant term on the left-hand side by adding 13 to both sides of the equation:13x−13+13=45+13\frac{1}{3}x – 13 + 13 = 45 + 1331x−13+13=45+13
This simplifies to:13x=58\frac{1}{3}x = 5831x=58
Now, to solve for xxx, multiply both sides of the equation by 3. Multiplying by 3 is necessary because the coefficient of xxx is 13\frac{1}{3}31, and multiplying by 3 will cancel the denominator:3⋅13x=3⋅583 \cdot \frac{1}{3}x = 3 \cdot 583⋅31x=3⋅58x=174x = 174x=174
Therefore, the original number is 174. This solution can be verified by substituting 174 back into the original condition: One-third of 174 is 58, and 58 minus 13 is indeed 45. The equation is satisfied, confirming the correctness of the solution.
