Tag: solution of a linear equation in one variable

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Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

On a car trip Sam drove  $m$  miles, Kara drove twice as many miles as Sam, and Darin drove  $20$  fewer miles than Kara. In terms of  $m$ , how many miles did Darin drive?

  1. $2m+20$
  2. $2m-20$
  3. $\frac{m}{2}+20$
  4. $\frac{m+20}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that

Number of miles driven by $Sam$ $=$ $m$
As $Kara$ drove twice as many miles as $Sam$,
Number of miles drove by $Kara$ $=$ $2m$
As $Darin$ drove 20 fewer miles than $Kara$,

Hence, Number of miles drove by $Darin$ $=$ Number of miles drove by $Kara$ $-$ $20$
$=$ $2m$ $-$ $20$ 
Therfore, $Darin$ drove $'2m$ $-$ $20'$ miles.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\cfrac{37}{4\sqrt{j}-19} = \cfrac{37}{17}$, then find the value of $j$.

  1. $64$
  2. $72.25$
  3. $81$
  4. $90.25$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\dfrac {{ 37 }}{{ (4\sqrt { j }  }-19)}={ 37 }/{ 17 }$

Since the numerators are equal, we can equate the denominators.
$\Rightarrow { (4\sqrt { j }  }-19)={ 17 }$
$\Rightarrow 4\sqrt { j } =36$
$\Rightarrow \sqrt { j } =9$
So, $j=81$
Hence, option C is correct.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\displaystyle \frac{a-b}{b}=\frac{3}{7}$, which of the following must also be true?

  1. $\displaystyle \frac{a}{b}=-\frac{4}{7}$
  2. $\displaystyle \frac{a}{b}=\frac{10}{7}$
  3. $\displaystyle \frac{a+b}{b}=\frac{10}{7}$
  4. $\displaystyle \frac{a-2b}{b}=-\frac{11}{7}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given: $\displaystyle \frac {a-b}{b}=\frac 37$

Separating denominators,

$\Rightarrow \displaystyle \frac ab -1=\frac 37$
$\Rightarrow \displaystyle \frac ab=\frac 37+1=\frac {10}{7}$
$\Rightarrow \dfrac {a}{b}=\dfrac {10}{7}$
Therefore, option B is correct.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $a\neq 0$ and $\dfrac{5}{x}=\dfrac{5+a}{x+a}$, what is the value of $x$?

  1. $-5$
  2. $-1$
  3. $5$
  4. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given:

$a$ $\neq$ $0$ and $\dfrac {5}{x}$ $=$ $\dfrac {5 \space + \space a}{x \space + \space a}$
To find the value of $x$,
$\Rightarrow \dfrac {5}{x}$ $=$ $\dfrac {5 \space + \space a}{x \space + \space a}$
$\Rightarrow 5$ $\times$ $(x$ $+$ $a)$ $=$ $x$ $\times$ $(5$ $+$ $a)$
$\Rightarrow 5x$ $+$ $5a$ $=$ $5x$ $+$ $xa$
Get the co-efficients of $'x'$ on one-side,
$\Rightarrow 5x$ $+$ $xa$ $-$ $5x$ $=$ $5a$
$\Rightarrow xa$ $=$ $5a$
As $(a$ $\neq$ $0)$,    $x$ $=$ $5$
Therefore, the value of $'x'$ is $'5'$.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

The total cost of three prizes is Rs. $2550$. If the value of second prize is $\left(\displaystyle\frac{3}{4}\right)^{th}$ of the first prize and the value of $3rd$ prize is $\displaystyle\frac{1}{2}$ of the second prize, then the value of the first prize is ___________.

  1. Rs. $1308$
  2. Rs. $1028$
  3. Rs. $1200$
  4. Rs. $1450$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

let the first,second and third prizes be $x,y$ and $z$ respectively

$x+y+z=2550$.....(1)
$y=\dfrac{3}{4}x$
$z=\dfrac{1}{2}y= \dfrac{3}{8}x$
Putting values of $y$ and $z$ in equation (1)
$x+\dfrac{3}{4}x+\dfrac{3}{8}x=2550$

$\dfrac{8x+6x+3x}{8}=2550$
$17x=2550\times8$
$x=1200$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\sqrt {x-1}- \sqrt {x+1}+1 =0$, then $4x$ is equal to ____. 

  1. $4 \sqrt {-1}$
  2. $0$
  3. $5$
  4. $1 \dfrac {1}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We can write it as $\sqrt{x-1} + 1 = \sqrt{x+1}$

Squaring both sides we get,
$x-1 + 1 +2\sqrt{x-1} = x+1$
$\Rightarrow 2\sqrt{x-1} = 1$

Squaring both sides, we get
$4(x-1) = 1$ 
$\therefore 4x = 5$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Solve the following linear equations. If $\cfrac{x-5}{3} = \cfrac{x-3}{5}$, then $x  $is equal to

  1. $8$
  2. $6$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given, $\cfrac { x - 5 }{ 3 }  =\cfrac { x-3 }{ 5 }$
Taking L.C.M., we get
$ \cfrac { 5x-25 }{ 15 }  = \cfrac { 3x - 9 }{ 15 } $
$5x - 25 = 3x -9$
Take $x$ terms on one sides and constants on another side, we get
$2x = 16$
$x = 8$