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Solved Problems

The following posts are word problems in Mathematics with a given solution. Thus, it is called "Solved Problems". To browse by topic or category, please use the drop-down menu above.

Algebra: Geometry Problem

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

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

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

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

A 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

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