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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### 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.
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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