Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Problem Statement:**
Two thirds of the sum of 36 and this unknown number is 28. Identify the unknown number.
**Solution Explanation:**
To find the unknown number, let's set up an equation based on the information provided.
1. Let \( x \) be the unknown number.
2. The sum of 36 and \( x \) is \( 36 + x \).
3. Two thirds of this sum is given as 28:
\[
\frac{2}{3}(36 + x) = 28
\]
4. To eliminate the fraction, multiply both sides by 3:
\[
2(36 + x) = 84
\]
5. Divide both sides by 2 to simplify:
\[
36 + x = 42
\]
6. Subtract 36 from both sides to solve for \( x \):
\[
x = 42 - 36
\]
7. Therefore, \( x = 6 \).
The unknown number is 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9163f72-9cb9-47ec-9932-aa32cb69a25b%2F18c2a931-7a0b-4c0d-b6e0-455fb711ac08%2Fclrn82e_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Two thirds of the sum of 36 and this unknown number is 28. Identify the unknown number.
**Solution Explanation:**
To find the unknown number, let's set up an equation based on the information provided.
1. Let \( x \) be the unknown number.
2. The sum of 36 and \( x \) is \( 36 + x \).
3. Two thirds of this sum is given as 28:
\[
\frac{2}{3}(36 + x) = 28
\]
4. To eliminate the fraction, multiply both sides by 3:
\[
2(36 + x) = 84
\]
5. Divide both sides by 2 to simplify:
\[
36 + x = 42
\]
6. Subtract 36 from both sides to solve for \( x \):
\[
x = 42 - 36
\]
7. Therefore, \( x = 6 \).
The unknown number is 6.
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