Algebra Word Problem Calculator

 

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Examples of Algebra Word Problem Calculator with Single Variable

Question 1. A father is four times as old as his child. In five years time, he will be 3 times as old as his child. What are their present ages.

Solution :

Present age Five year hence

Let the child's present age be `= x`  years
`:.`  The father's present age `= 4x`  years

Child's age `= (x + 5)`  years
Father's age `= (4x + 5)`  years

 

In five years time, father will be 3 times as old as his child.
Father's age = three times his child's age
`:. 4x + 5 = 3(x + 5)`
`4x + 5 = 3x + 15`

 `:. 4x - 3x = 15 - 5`

`x = 10`

Child's age `=` `10` years
Father's age `=` `4x`
`= 4(10)`
`= 40` years

Question 2. Mrs Sharma is now twice as old as her neighbour. Twelve years ago she was three times as old as her neighbour then. How old are they now?

Solution :

 

Mrs sharma

Neighbour

Let Mrs sharma's age be `2x`

Mrs sharma's age `12` years ago `= 2x - 12`

Let neighbour's age be `x`

Neighbour's age `12` years ago `= 3(x - 12)`



NOTE : - As Mrs Sharma's age was three time that of her neighbour twelve years ago, therefore,

`2x - 12 = 3(x - 12)`

`2x - 12 = 3x - 36`

`2x - 3x = -36 + 12`

`-1x = -24`

`x = 24`

 

`:.` Neighbour's age `= 24` years

and Mrs Sharma's age `= 2x`

`=2(24)`

`= 48` years

Examples of Algebra Word Problem Calculator with Two variable equation solver

 

 

Question 3. In 4 years time, a father will be 3 times the age of his son; 4 years ago he was 5 times the age of his son. What are their present age?

 

 

Present Age

Age 4 years hence

Age 4 years ago

Father

Son

`x`

`y`

`x + 4`

`y + 4`

`x - 4`

`y - 4`

 

 

4 years hence, father will be 3 times the son's age.

That is, `x + 4 = 3(y + 4)`

`:. x + 4 = 3y + 12`

`:. x - 3y = 12 - 4`

`:. x - 3y = 8` ...equation number (1)

 

4 years ago, father was 5 times the son's age.

That is, `x - 4 = 5(y - 4)`

`:. x - 4 = 5y - 20`

`:. x - 5y = -20 + 4`

`:. x - 5y = -16` ...equation number (2)

 

Solve equation (1) and (2)

 

`x - 3y = 8` ...equation number (1)

`x - 5y = -16` ...equation number (2)

Subtracting equation (2) from (1), we get,

`+2y = 24`

`:. y = 24/2`

`:. y = 12`

 

Substituting y = 12 in equation (1)

`x - 3y = 8`

`:. x - 3(12) = 8`

`:. x - 36 = 8`

`:. x = 8 + 36`

`:. x = 44`

 

Ans : Father's present age is 44 years and son's present age is 12 years.