Respuesta :
Answer:
80 Questions
Step-by-step explanation:
First 20/32
then 3/4 questions wrong
so let's say he got there were 48 remaining questions
then he would have 36 wrong and and 12 correct
therefore it would be..
20 + 12/32 + 48
32/80
__________________________________________
so let's check the answer
it says he got 40%
so let's do 32/80
= 0.4
to convert it into percentage times by 100
= 0.4 x 100
= 40%
Answer:
There are [tex]80[/tex] questions on this exam.
Step-by-step explanation:
Let [tex]x[/tex] denote the number of questions on this exam in total (including the first [tex]32[/tex] questions.)
There would be [tex](x - 32)[/tex] questions after the first [tex]32[/tex].
Since the student got three-quarters of these wrong, only one-quarter ([tex]1 - (3/4) = (1/4)[/tex]) of these [tex](x - 32)[/tex] questions are correct. That would be another [tex](1/4) \cdot (x - 32)[/tex] right answers.
In total, the number of questions that the student got correct would be:
[tex]\begin{aligned} & 20 + \frac{1}{4} \cdot (x - 32) \\ =\; & 20 + \frac{x}{4} - 8 \\ =\; & 12 + \frac{x}{4}\end{aligned}[/tex].
On the other hand, it is given that the student got [tex]40\%[/tex] of the [tex]x[/tex] questions right. Hence, the number of correct answers may also be expressed as:
[tex]\begin{aligned} & (40\%) \, x\\ =\; & \frac{2\, x}{5} \end{aligned}[/tex].
Both expressions give the number of correct answers. Equate the two expressions and solve for [tex]x[/tex]:
[tex]\displaystyle 12 + \frac{x}{4} = \frac{2\, x}{5}[/tex].
[tex]\displaystyle \left(\frac{2}{5} - \frac{1}{4}\right)\, x = 12[/tex].
[tex]\displaystyle \frac{8 - 5}{20}\, x = 12[/tex].
[tex]\displaystyle \frac{3}{20}\, x = 12[/tex].
[tex]\begin{aligned} x &= 12 \times \frac{20}{3} \\ &= 80\end{aligned}[/tex].
In other words, there are [tex]80[/tex] questions on this exam in total.
