Tag: calculations and mental strategies 1

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

  1. $32$ years
  2. $36$ years
  3. $44$ years
  4. $40$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
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.   

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

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:

  1. $45m$
  2. $60m$
  3. $75m$
  4. $120m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Parallel sides $= 5x,\, 3x$
area $=\dfrac{24}{2}(5x+3x)=1440 $
$12(8x)=1440$
$x=\dfrac{120}{8}=15$ 
$5x=15\times 5$ 
     $=75m$
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

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

  1. $\dfrac { 2 } { 3 }$
  2. $\dfrac { 3 } { 4 }$
  3. $\dfrac { 2 } { 5 }$
  4. $\dfrac { 1 } { 4 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
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]

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

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

  1. $2x-13=17$
  2. $13-2x=17$
  3. $2x-17=13$
  4. $2x+13=17$
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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