Tag: maths

Questions Related to maths

Reduce the linear equation: $x + 3-\dfrac{2x}{3}+\dfrac{x}{6}=0$

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

  1. $x=12$

  2. $x=10$

  3. $x=8$

  4. $x=-6$

Show answer
Correct Option: D
Explanation:

Given, $x + 3-\dfrac{2x}{3}+\dfrac{x}{6}=0$
L.C.M of the denominator $3$ and $6$ is $6$.
Multiplying both the sides by $6$, we get
$6x + 18 - 4x + x = 0$
$7x - 4x + 18 = 0$
$3x = -18$
$x = -6$

Reduce the linear equation: $\dfrac{x}{2}+\dfrac{2x}{4}= 10$

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

  1. $x=6$

  2. $x=7$

  3. $x=8$

  4. $x=10$

Show answer
Correct Option: D
Explanation:

Given, $\dfrac{x}{2}+\dfrac{2x}{4}= 10$
L.C.M of the denominator $2$ and $4$ is $4$.
Multiplying both the sides by $4$, we get
$2x + 2x = 40$
$4x = 40$
$x = 10$

A brand new car costs $ \$35,000$. For the first $50,000$ miles, it will depreciate approximately $\$0.15$ per mile driven. For every mile after that, it will depreciate by $\$0.10$ per mile driven until the car reaches its scrap value. Find the net worth of the car after it is driven $92,000$ miles.

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

  1. $\$11,300$

  2. $\$13,800$

  3. $\$17,000$

  4. $\$23,300$

Show answer
Correct Option: D
Explanation:

Given the cost of car $=\$35000$

First $50000$ miles it will depreciated app $\$ 0.15$ per mile 
And After that it will depreciate by $\$0.10$ per miles 
Then  depreciate after $50000$ miles $=$  $50000\times $0.15=$7500$
And depreciate after $92000-50000=42000$ miles $= $ $42000\times $0.10=$4200$
Total  depreciate after $92000$ mole $=7500+4200=\$11700$
Then worth after it is driven $92000=35000-11700=\$23300$

If  $\sqrt{x+16} = x-4$, then the value of extraneous solution of the above equation is:

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

  1. $0$

  2. $4$

  3. $5$

  4. There are no extraneous solutions

Show answer
Correct Option: A
Explanation:
Given, $\sqrt{x+16}=x-4$
Squaring both sides, we get
$x+16=(x-4)^{2}$
$\Rightarrow x+16=x^{2}-8x+16$
$\Rightarrow x^{2}-8x-x=16-16$
$\Rightarrow x^{2}-9x=0$
$\Rightarrow x(x-9)=0$
Then $x=0$ or $x=9$

A neighborhood recreation program serves a total $280$ children who are either $11$ years old or $12$ years old. The sum of the children's ages is $3,238$ years. How many $11$ year old children does the recreation program serve?

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

  1. $54$

  2. $122$

  3. $132$

  4. $158$

  5. $208$

Show answer
Correct Option: B
Explanation:

Let the number of $11$ years children is $x$ and $12$ year children is $y$.

$\therefore  11x+12y=3238$.....(1)
$\Rightarrow x+y=280$
$\Rightarrow y=280-x$
Sustitute the value of $y$ in (1)
$\Rightarrow 11x+12(280-x)=3238$
$\Rightarrow 11x+3360-12x=3238$
$\Rightarrow 11x-12x=3238-3360$
$\Rightarrow x=122$
Hence, number of $11$ year children are $122$. 

If $3^{2x + 2} = 27^{2}$, find the value of $x$.

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

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: C
Explanation:

Given, $3^{2x+2}=27^{2}$ 

$3^{2x+2}=3^{6}$
Taking $\log$ on both sides give us 
$(2x+2)\log 3=6\log 3$
$\Rightarrow 2x+2=6$ 
$\Rightarrow x=2$

If $2^{x} + 2^{x + 2} = 40$, then the value of $x$ is

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:

Given, ${ 2 }^{ x }+{ 2 }^{ x+2 }=40\ \Rightarrow { 2 }^{ x }+{ 2 }^{ 2 }{ 2 }^{ x }=40\ \Rightarrow { 2 }^{ x }+(4){ 2 }^{ x }=40\ \Rightarrow (5){ 2 }^{ x }=40\ \Rightarrow { 2 }^{ x }=8\ \Rightarrow { 2 }^{ x }={ 2 }^{ 3 }$

So, $ x=3$

When a number $x$ is subtracted from $36$ and the difference is divided by $x$, the result is $2$. Find the value of $x$.

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

  1. $2$

  2. $4$

  3. $6$

  4. $12$

Show answer
Correct Option: D
Explanation:

According to the question:

$ \dfrac { 36-x }{ x } =2\ \Rightarrow 36-x=2x\ \Rightarrow 36=3x$
$ \Rightarrow x=12$

If $3^{n - 3} + 3^{2} = 18$, calculate the value of $n$.

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$

Show answer
Correct Option: E
Explanation:

Given, ${ 3 }^{ n-3 }+{ 3 }^{ 2 }=18$

$ { 3 }^{ n-3 }+9=18$
${ 3 }^{ n-3 }=18-9=9$
$ { 3 }^{ n-3 }={ 3 }^{ 2 }$
So, $ n-3=2$
$n=5\ $

Let $a, b$ and $c$ be non-zero numbers such that $c$ is $24$ greater than $b$ and $b$ is $24$ greater than $a$. If $\dfrac {c}{a} = 3$, then find the value of $b$.

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

  1. $-48$

  2. $-24$

  3. $24$

  4. $48$

Show answer
Correct Option: D
Explanation:

Let the value of $a$ be $x$

Thus, $b$ would be $24+x$
and $c$ is $24+24+x=48+x$.
Given, $\dfrac {c}{a}=3$
Therefore, $\dfrac {48+x}{x}=3$
$\Rightarrow 2x=48$
$\Rightarrow x=24$
Value of $b$ is $24+x=24+24=48$.