Tag: forming equations from statements

Questions Related to forming equations from statements

Four years ago, the father's age was three times the age of his son. The total of the age of the father and the son after four years will be $64$ years. What is the father's age at present?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $32$ years

  2. $36$ years

  3. $44$ years

  4. $40$ years

Show answer
Correct Option: D
Explanation:

fathers present age $= x$ years.

sons present age $= y$ years.  

four years ago, fathers age $=3 \times $ sons age.
$(x-4)=(y-4)\times 3$
$x=3y-8$.....(i) 

after 4 years, fathers age$ +$ sons age $= 64 $
$x+4+y+4=64 $
$x+y=56$.....(ii) 

solve for $x$
$x=3\times 56-3x-8$ 
$4x=160$ 
$x=40$ years  

D is correct.   

The area of a field in the shape of a trapezium measures $1440{m}^{2}$. The perpendicular distance between its parallel sides is $24m$. If the ratio of the parallel sides is $5:3$, the length of the longer parallel side is:

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $45m$

  2. $60m$

  3. $75m$

  4. $120m$

Show answer
Correct Option: C
Explanation:
Parallel sides $= 5x,\, 3x$
area $=\dfrac{24}{2}(5x+3x)=1440 $
$12(8x)=1440$
$x=\dfrac{120}{8}=15$ 
$5x=15\times 5$ 
     $=75m$

If $\left(\dfrac { 3 } { 4 }\right)^{th}$ of $x$ of $\left(\dfrac { 1 } { 4 }\right)^{th}$ of $35600 = 1668.75 ,$ find $x$

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $\dfrac { 2 } { 3 }$

  2. $\dfrac { 3 } { 4 }$

  3. $\dfrac { 2 } { 5 }$

  4. $\dfrac { 1 } { 4 }$

Show answer
Correct Option: D
Explanation:

$\dfrac { 3 }{ 4 } \times x\times \dfrac { 1 }{ 4 } \times 35600=1668.75$

$\Rightarrow x=\dfrac { 1668.75\times 16 }{ 3\times 35600 } =\dfrac { 1 }{ 4 } $      [D]

If a function $f$ is linear with $f(0)=5$ and $f(2)=9$ then find $f(9)$

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 23

  2. 25

  3. 26

  4. none of these

Show answer
Correct Option: A
Explanation:

$f$ is a linear function 

So Let $f=ax+b$
$f(0)=a(0)+b=5\\implies b=5\cdots(1)\f(2)=9\a(2)+5=9\\implies a=2\f(x)=2x+5\f(9)=2(9)+5\18+5=23$

If $(30 + x) : (23 + x) = 5 : 4$ then find the value of x.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 5

  2. 6

  3. 4

  4. 7

Show answer
Correct Option: A
Explanation:

$ => 30 + x : 23 + x = 5:4 $


$ => \frac {30 + x}{23 + x} = \frac {5}{4} $

Cross multiplying, 

$ 120 + 4x = 115 + 5x $


$ 120 - 115 = 5x - 4x $


$ x = 5 $

Translate the following sentence into an algebraic equation: "13 diminished from twice a number is equal to 17"

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $2x-13=17$

  2. $13-2x=17$

  3. $2x-17=13$

  4. $2x+13=17$

Show answer
Correct Option: A
Explanation:

Let  the  number  be  $x.$


Twice  of  the  number  is  $2x$  and  $13$  is  diminished  from  $2x$  means  $(2x-13)$  and  it  is  equal   to   $17. $
 So  answer  is  option  A

'8 is less than twenty times a' is written as 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 8 - 20a

  2. 20ac

  3. 8 < 20 $\times$ a - 8

  4. 20a - 8

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Correct Option: D
Explanation:

Eq : 20a - 8

Algebraic expression for the statement 8 times a taken away from 60 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 8a - 60

  2. 60 - 8a

  3. 0

  4. 60a - 8

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Correct Option: B
Explanation:

Eq : 20a - 8

The equation for the statement : 'half of a number added to 20 is 25' 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $\displaystyle{\frac{x}{4}}$ + 20 = 25

  2. $\displaystyle{\frac{x}{5}}$ + 25 = 20

  3. $\displaystyle{\frac{x}{2}}$ + 20 = 25

  4. $\displaystyle{\frac{x}{3}}$ + 20 = 25

Show answer
Correct Option: C
Explanation:

$\displaystyle{\frac{x}{2}}$ + 20 = 25 

Half of the number added to 20 will give the answer 25
$\dfrac{10}{2} +20=25$

Equation of the statement : 'Thrice the length of a room is $240$ metres.' 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $3l = 240$

  2. $3 + l = 40$

  3. $3l = 420$

  4. None of these

Show answer
Correct Option: A
Explanation:

Let $l$ be the length of a room 

therefore according to statement, required equation is   
$3l = 240 $