# Solved Problem: Algebra Number Problem

Submitted by JM on Tue, 07/28/2009 - 09:43**Number Problem**

The smaller of two numbers is 9 less than the larger, and their sum is 37.

Find the numbers.

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

Let

$ \mathbf{x} $ = smaller number

$ \mathbf{y} $ = bigger number

$ x = y – 9 $

Hence, **Read more »**

# 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**

# Uniform-Motion Problem: Unknown Rates

Submitted by JM on Fri, 07/17/2009 - 23:31Peter and her daughter Liza leave home at the same time in separate cars. Peter drives to his office, a distance of **28 km**, and Liza drives to school, a distance of **36 km**. ** They arrive at their destinations at the same time.** What are their average rates if Peter’s average rate is 10km/hr less than his daughter’s?

**Solution:**

We need to determine the average rates of Liza and Peter; therefore, we make the following representations:

$\mathbf{r:}$ the number of kilometers per hour in Liza’s average rate

$\mathbf{r - 10:}$ the number of kilometers per hour in Peter’s average rate