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How to Solve Math Word Problems

A lot of students struggle with solving Word Problems. The objective of this lesson is to help you understand what exactly the word problem is asking and how to go write that in Mathematical terms so that you can solve it.

Remember that no matter how hard a word problem appears, the simple fact is that there will always be words to help you solve it!!! You already know those words,all that remains is for you to write it down correctly.

What they Say/What they Mean
The people who set Word problems have only 1 goal–To confuse you. So they try to use words that appear confusing.Unfortunately, they are limited by the rules of Mathematics. The rules are clear and simple. There is/can be no confusion about them.

What They Say	What they Mean	Examples
“ Decreased by”	“–” (be careful of the order)	5 decreased by 3=>5-3(Note the order)
“Difference”	“–” (be careful of the order)	The difference between a and b=>a-b
“Equals”	“=”	a equals b=>a=b
“ Increased by”	“+”	a is increased by b =>a+b
“Is”	“=”	The value of a is X=>a=X
“ Less than”	“–” (be careful of the order)	a is less than b by 5=>b-a=5
“More than”	“+”or”-” (depends on how you write it)	a is more than b by 2=>a-2=b or b+2=a
“Of”	“X”,“·”,“times”
“Product”	“X”, “·”,“times”	The product of a and b=>axb=a.b
“Perimeter”	“Sum of the sides”
“Quotient”	“÷”	The quotient of a and b=>a/b
“Such that”	this is where your equation gets created
“Sum”	“+”
“Times”	“Two times”or“2·_____”

So now we know what certain terms in a problem mean, let’s take a look at solving some of these problems.

How to Solve Age Problems:

Q.Four years from now,Peter’s age will be 4 times his son’s age. Twelve years from now he will be 2.5times his son’s age.Find their present ages.

Solution:
“Hmm, I’ve read the problem but I dont know where to begin”. We’ve heard that far too many times. When you dont know something, like the Detectives in CSI/Criminal Minds/(Insert favourite Detective Serial here) just put down X. If there’s more, use another alphabet say Y!
So,
Let Peter’s Present Age = X
His Son’s Present Age = Y

Four years from now
Peter’s age = X+4
His son’s age = Y+4

Now go back to the problem and read the first line

“Four years from now,Peter’s age will be 4 times his son’s age”

“Four years from now,Peter’s age” +”will be” +”4 times his son’s age”
_____________”X+4″___________”=”________ “4(Y+4)”
(Remember that the first line said 4 years from now which means that even the son would have aged by 4 years)

X+4 = 4(Y+4)
=>X-4Y = 12 —(1)

“Twelve years from now he” +”will be” + “2.5times his son’s age” __________”X+12″________”=”_______2.5(Y+12)

X+12=2.5(Y+12)=>2X-5Y = 36 —(2)

We know have 2 equations and 2 unknowns.Which is good. For all the unknows in a problem, we require that many equations. So if there were 3 unknowns,we would require 3 equations to solve them.

Solving (1) and (2) we get
y =4 which means X = 28

Q2.The present age of a father is 10times his son’s age. In 6 years, his age will be four times his son’s age. What are their present ages?

Solution:

As always, we start by defining the unknown
Let the father’s present age = X
Son’s Present age = Y

“The present age of a father is 10times his son’s age”

Whenever you get stuck converting something like “age is 10times”, then just use numbers, eg

If the son was 2, then 10times his age would be (2+2+2…10times OR 2*10) –> 20
so, IF he was y, then 10times his age would be (y+y….10times OR 10*y) –> 10y
X =10Y

“In 6 years, his age” +”will be”+ “four times his son’s age”
_______”X+6″______=________4 (Y+6)
X+6=4(Y+6)
=>X-4Y = 18

We now have our required two equations
X =10Y
X-4Y = 18

Solving we get
X = 30 and Y = 3