Question

An exam has 60 questions. Phelix got 85% correct. How many questions did he answer correctly?

Answer 1

Hint: let us assume that the number of questions Phelix got correct be x. given, 85% of the total question is correctly done by Phelix. The total number of questions is 60. Therefore, 85% of 60 questions is \[\dfrac{85}{100}\times 60\]. Equate this expression to x and find the value of x which is the required answer.

Complete step-by-step solution:
According to the question, we are asked to find the total number of questions Phelix answered correctly.
We have been given the total number of 60 questions.
And 85% of the total questions are correctly answered by Phelix.
Let us assume x to be the total number of questions correctly done by Phelix.
But we know that the total number of correct answers is 85% of 60 questions.
On expressing the given situation into an equation with variable x, we get
x=85% of 60 questions.
We know that \[85%=\dfrac{85}{100}\].
And 85% of 60 questions is \[\dfrac{85}{100}\times 60\].
Therefore, we get
\[x=\dfrac{85}{100}\times 60\]
We can write \[60=6\times 10\] and \[100=10\times 10\]. We get
\[\Rightarrow x=\dfrac{85}{10\times 10}\times 6\times 10\]
Cancelling out the common term 10 from the numerator and denominator, we get
\[\Rightarrow x=\dfrac{85}{10}\times 6\]
We can further simplify the expression as
\[\Rightarrow x=\dfrac{85}{5\times 2}\times 3\times 2\]
Cancelling out 2 from the numerator and denominator, we get
\[\Rightarrow x=\dfrac{85}{5}\times 3\]
85 can be written as the product of 5 and 17.
\[\Rightarrow x=\dfrac{17\times 5}{5}\times 3\]
Cancelling 5 from the numerator and denominator, we get
\[\Rightarrow x=17\times 3\]
\[\therefore x=51\]
Hence, the total number of questions Phelix got correct out of 60 questions is 51.

Note: We should not simply multiply 85 with 60 to get the answer. 85 should be divided by 100, since percentage is mentioned in the question. Also 85% of 60 do not mean 85% added with 60. It means 85% multiplied with 60. Avoid calculation mistakes during multiplication. Solve the answer step by step to avoid confusion.