# Homework

Author

Jaime Carlos M Infante

License

Creative Commons CC BY 4.0

Abstract

It is a math template. It's not the best .

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Author

Jaime Carlos M Infante

License

Creative Commons CC BY 4.0

Abstract

It is a math template. It's not the best .

```
\documentclass[12pt]{article}%
\usepackage{amsfonts}
\usepackage{fancyhdr}
\usepackage{comment}
\usepackage[a4paper, top=2.5cm, bottom=2.5cm, left=2.2cm, right=2.2cm]%
{geometry}
\usepackage{times}
\usepackage{amsmath}
\usepackage{changepage}
\usepackage{amssymb}
\usepackage{graphicx}%
\setcounter{MaxMatrixCols}{30}
\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Z}{\mathbb{Z}}
\begin{document}
\title{Homework}
\author{Jaime Carlos M Infante}
\date{\today}
\maketitle
\section{Example}
All problems like the following lead eventually to an equation in that simple form.
\subsection{Problem 1}
Jane spent \$42 for shoes. This was \$14 less than twice what she spent for a blouse. How much was the blouse?
\subsection{Solution}
Every word problem has an "unknown number".In this problem,it is the price of the blouse. Always let "x" represent the "unknown number".That is, let "x" answer the question.
\subsection{Solution part 2}
Let x,then,be how much she spent for the blouse.The problem states that "This"--that is, \$42--was \$14 less than two times x.
Here is the Equation: 2x-14= 42
2x=42+14
=56
x=56/2
=28
\section{Example 2}
There are "b" boys in the class. This is three more than the number four times the number of girls.
\subsection {Solution}
Again let "x" represent the unknown number that you are asked to find: Let X be the number of girls. The problem states that "This"--b--is three more than 4 times X.
4x+3=b
4x=b-3
x=b-3/4
The solution here is not a number,because it will depend on the value of b. This is a type of a literal equation, which is very common in algaebra.
\section{Example 3. The whole is equal to the sum of the parts}
The sum of two numbers is 84,and one of them is 12 more than the other. What are the two numbers?
\subsection{Solution}
In tis problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then,be the first number.
we are told that the other number is 12 more,x+12.
the problem states that their sum is 84:
x+x+12=84
The line over x+12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x=84-12
=72
x=72/2
x= 36
This is the first number. Therefore the other number is:
x+12= 36+12= 48
the sum of 36+48 = 84
\section{Example 4}
The sum of two consecutive numbers is 37. What are they?
\subsection{Solution}
Two consecutive numbers are 8 and 9, or 51 and 52. Let x, then, be the first number. Then the number after it is x + 1. The problem states that their sum is 37:
x + x + 1= 37
2x = 37-1
= 36
x = 36 / 2
= 18
The two numbers are 18 and 19.
\section{Example 5}
One number is 10 more than another. The sum of twice the smaller plus three times the larger,is 55. What are the two numbers?
\subsection{Solution}
Let x be the smaller number.
Then the larger number is 10 more: x + 10
The problem states:
2x + 3(x + 10)= 55
That implies...
2x + 3x + 10 = 55 . Lesson 14
5x = 55 - 30 = 25
x = 5
That's the smaller number.The larger number is 10 more:15
\section{Example 6}
Divide \$80 among three people so that the second will have twice as much as the first, and the third will have \$5 less than the second.
\subsection{Solution}
Again qwe are asked to find one more number. We must begin by letting x be how much the first person gets.
Then the second gets twice as much : 2x.
and the third gets \$5 less than that: 2x-5 .
Their sum is \$80:
x + 2x + 2x - 5 = 80
5x = 80 + 5
x = 85 / 2
= 17
This is how much the first person gets. Therefore the second gets:
2x = 34 .
and the thirs gets
2x - 5 = 29 .
The sum of 17, 34, and 29 is in fact 80.
\end{document}
```