TRANSLATING WORD PROBLEMS INTO EQUATIONS

Translating a sentence or statement into an algebraic equation is an important stuff which is much required to solve word problems in math. 

Let us see, how to translate the information given in a word problem into an algebraic expression or equation in the following examples. 

Example 1 :

Example 2 :

Example 3 :

Example 4 :

Example 5 :

Translating Word Problems into Equations Step by Step

Problem :

The age of a father is thrice the sum of the ages of his two sons and 5 years hence his age will be twice the sum of their ages. Find the present age of the father.

Solution :

Step 1 :

Let us understand the information given.

There are two information given in the question. 

1. The age of the father is thrice the sum of the ages of his two sons. (At present)

2. After 5 years, his age would be twice the sum of their ages. (After 5 years)

Step 2 :

Target of the question : Present age of the father

Step 3 :

Introduce required variables for the information given in the question. 

Let x be the present age of the father.

Let y be the sum of present ages of two sons.

Clearly, the value of x to be found.

Because that is the target of the question.

Step 4 :

Translate the given information as mathematical equation using x and y. 

First information :  

The age of the father is thrice the sum of the ages of his two sons.

Translation (i) :

The Age of the father ----->  x

is ----->  =

Thrice the sum of the ages of his two sons ----->  3y 

Equation related to the first information using x and y is

x  =  3y -----(1)

Second Information :

After 5 years, his age would be twice the sum of their ages.

Translation (ii) :

Age of the father after 5 years ----->  (x + 5)

After 5 years :

Sum of the ages of his two sons ----->  y + 5 + 5  =  y + 10

(Here we have added 5 two times.The reason is there are two sons)

Twice the sum of ages of two sons -----> 2(y + 10)

would be ----->  =

Equations related to the second information using x and y is

x + 5  =  2(y + 10)

Simplify.

x + 5  =  2y + 20

Subtract 2y and 5 from each side.

x - 2y  =  15 -----(2)

Step 5 :

Solve (1) and (2) to find the value of the unknown.

Substitute 3y for x in (2).

(2)-----> 3y - 2y  =  15

y  =  15

Substitute 15 for y in (1).

(1)-----> x  =  3(15)

x  =  45

Therefore, the present age of the father is 45 years.

Apart from the stuff given in this section, if you would like to have any other stuff in math, please use our google custom search here. 

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

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Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6