19 cookies, ho 10. The sum of three numbers is 161. The second number is 7 more than the first number, and the third number is 5 times the first 2nd number. Find the second number. = 3rd angles of a triangle is 10. 11.
19 cookies, ho 10. The sum of three numbers is 161. The second number is 7 more than the first number, and the third number is 5 times the first 2nd number. Find the second number. = 3rd angles of a triangle is 10. 11.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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
Transcribed Image Text:### Problem Statement:
**Question 10:**
The sum of three numbers is 161. The second number is 7 more than the first number, and the third number is 5 times the first number. Find the second number.
### Mathematical Formulation:
- Let the first number be denoted as \( x \).
- The second number, being 7 more than the first, is represented as \( x + 7 \).
- The third number, being 5 times the first, is represented as \( 5x \).
### System of Equations:
Formulate the equation based on the given problem:
- \( x + (x + 7) + 5x = 161 \)
Simplifying:
1. Combine like terms:
\( 7x + 7 = 161 \)
2. Subtract 7 from both sides:
\( 7x = 154 \)
3. Divide by 7 to isolate \( x \):
\( x = 22 \)
### Solution:
With \( x = 22 \):
- Calculate the second number:
\( x + 7 = 22 + 7 = 29 \)
Thus, the second number is **29**.
### Additional Notes:
This problem involves setting up a simple linear equation to solve for unknown values, highlighting relationships between different quantities. Solutions require algebraic manipulation to determine unknown variables.
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