# Solved Problems

# Algebra: Geometry Problem

Submitted by JM on Tue, 07/28/2009 - 15:06**Algebra: Geometry Problem
**

If the

**width**of a rectangular field is

**2 meters**more than

**one-half**of its

**length**and its perimeter is

**40 meters**, what are the dimensions?

**Solution:**

From the problem statement, we can derive the following representation:

Let:

**L =**length of the field

**W =**width of the field

**P = 2L + 2W**

Hence,

# Algebra: Number Problem

Submitted by JM on Tue, 07/28/2009 - 10:40**Solved Problem: Number Problem 2**

Find three consecutive even integers whose sum is 138.

**Solution:**

Consecutive numbers are just the series of counting numbers. However, in this particular problem, the unknown consecutive numbers are restrictive to even numbers only. In this case, the numbers are incremented by **2**. For instance, if the first even number is **60**, the next two consecutive even numbers are **62 (from 60 + 2)** and **64 (from 60 + 4)**.

From the problem statement above, the following representation can be derived as follows:

Let the following be the consecutive numbers

# Another Simple Number Problem

Submitted by JM on Mon, 07/27/2009 - 23:21**Another Simple Number Problem
**Find two numbers whose sum is

**7**provided that one is

**3**times the other.

**Solution:**

Based on the problem statement, the following representation is derived:

Let

$\mathbf{x}$ = first number

$\mathbf{y}$ = second number

$x = 3y$

Hence,

$ x = 3y $ Eq. 1

$ x + y = 7 $ Eq. 2

Equating

**Eq. 1**to zero and multiplying the result with

**-1**and adding with

**Eq. 2**becomes

\[ (x – 3y = 0)(-1) \]

\[ -x + 3y = 0 \]

# Simple Number Problem

Submitted by JM on Mon, 07/27/2009 - 22:54**Simple Number Problem
**The sum of two numbers is 9 and their difference is 6. What are the numbers?

**Solution:**

This simple number problem calls for two variable representation, say

**x**and

**y**.

Let

$\mathbf{x}$ = first number

$\mathbf{y}$ = second number **Read more »**

# Work Problem

Submitted by JM on Sat, 07/18/2009 - 22:48A **work problem** is one in which a specific job is done in a certain length of time when a uniform rate of work is assumed. For example, if it takes a man 10 hours to paint a room, then his rate of work is $\frac{1}{10}$ of the room per hour.

To solve a work problem, we need to multiply the **rate of work **by the **time **to obtain the **fractional part **of work completed. Like in the example above, if the painter works for 7 hours, then the fractional part of the work completed is $\frac{7}{10}$.

**Work Problem**