Question

Sue answered 80% of 150 test questions correctly. How many questions did she not answer correctly?

Answer 1

There are many formulas for percentage problems. Here, we will use the most basic formula as $Y = P\% \times X$. Where X and Y are numbers and P is the percentage. In this question, 80% of 150 test questions are correct that also means 20% of 150 test questions are not correct. So, we will find 20% of 150.

Complete step-by-step answer:
In this question, given that 80% of 150 test questions are correct.
And want the number of questions that she did not answer correctly.
Here, 80% of 150 test questions are correct that also means 20% of 150 test questions are not correct.
So, we will find 20% of 150 to solve this question.
Now, let us use the basic formula of percentage.
$Y = P\% \times X$
In the above formula, the value of X is 150 and the value of P is 20.
$\Rightarrow Y = 20\% \times 150$ ....(1)
Let us convert 20% to decimal by removing the percentage sign and divide by 100. That is
$\Rightarrow 20\% = \dfrac{{20}}{{100}}$
Therefore,
$\Rightarrow 20\% = 0.20$
Now, let us put the value of 20% in equation (1).
$\Rightarrow Y = 0.20 \times 150$
So, the answer will be
$\Rightarrow Y = 30$

Hence, we can say that Sue did not answer 30 questions correctly among 150 questions.

Note:
Here, we can also find the value of 80% for correct answers and then subtract the answer from 150.
Let us calculate80% of 150.
$Y = P\% \times X$
In the above formula, the value of X is 150 and the value of P is 80.
$\Rightarrow Y = 80\% \times 150$ ....(1)
Let us convert 20% to decimal by removing the percentage sign and divide by 100. That is
$\Rightarrow 80\% = \dfrac{{80}}{{100}}$
Therefore,
$\Rightarrow 80\% = 0.80$
Now, let us put the value of 80% in equation (1).
$\Rightarrow Y = 0.80 \times 150$
So, the answer will be
$\Rightarrow Y = 120$
That means 120 answers are correct.
So, incorrect answers are:
$\Rightarrow 150 - 120$
That is
$\Rightarrow 30$