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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

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.

  1. $\$11,300$
  2. $\$13,800$
  3. $\$17,000$
  4. $\$23,300$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $92000=35000-11700=\$23300$

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

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

  1. $0$
  2. $4$
  3. $5$

  4. There are no extraneous solutions
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $x=9$
Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

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?

  1. $54$
  2. $122$
  3. $132$
  4. $158$
  5. $208$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $122$. 

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

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

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

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

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 $b$.

  1. $-48$
  2. $-24$
  3. $24$
  4. $48$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $24+x=24+24=48$.