Respuesta :

Answer is  7:13

======================================================

Explanation:

He answered 5/7 of the 35 short-answer questions correctly. So he got (5/7)*35 = 25 of those questions correct. At 2 marks each for these questions, he earned 25*2 = 50 points from this group alone.

There are 35 short-answer questions and 15 long-answer questions. That's 35+15 = 50 questions total.

We're told that he answered 60% of all the questions correctly. So he answered 0.60*50 = 30 questions correctly.

Earlier we found that he answered 25 short-answer questions, which must mean he got 30-25 = 5 long-answer questions done correctly. At 4 marks a piece, Keith earns 5*4 = 20 points in this group.

So overall, he earned 50+20 = 70 points from both types of questions.

---------------------

If he got all answers correct, then he would earn 35*2 = 70 points from the short-answer questions and 15*4 = 60 points from the long-answer questions. That's a total of 70+60 = 130 points to get a perfect score.

The ratio of his score to the perfect score is 70:130 which reduces to 7:13 when dividing both parts by the GCF 10.

sqdancefan

9514 1404 393

Answer:

  70/130 . . . . reduces to 7/13

Step-by-step explanation:

Strategy

The problem statement describes 2 kinds of quiz questions, and different relations regarding the numbers of questions answered correctly. The problem asks for the number of marks Keith had relative to the total number of marks.

This means you need to find Keith's marks and the available marks for each question type (4 numbers).

Because of the way the problem tells you the number of long-answer questions answered, additional computations are required to find the total number of questions Keith answered and the number of short-answer questions Keith answered. (The difference of these is the number of long-answer questions answered.) That's 3 more computations.

You have to keep in mind the purpose of each computation and how it fits in to the final result. This is why we label the intermediate results.

Solution

Short Answer Marks

There were 35 short-answer questions for 2 marks each. That's a total of ...

  (35)(2) = 70 . . . . marks for all short-answer questions

Keith got 5/7 of those, so got ...

  (5/7)×70 = 50 . . . . Keith's marks for short-answer questions.

__

Long Answer Marks

There were 15 long-answer questions for 4 marks each. That's a total of ...

  (15)(4) = 60 . . . . marks for all long-answer questions

The total number of questions on the quiz was 35 +15 = 50. Keith answered 60% of them, so answered ...

  0.60×50 = 30 . . . . total number of questions Keith answered

We know Keith answered (5/7)(35) = 25 short-answer questions, so must have answered 30-25 = 5 long-answer questions. His marks for those were ...

  (5)(4) = 20 . . . . Keith's marks for long-answer questions

__

Total Marks

Then the total number of marks for all answers on the quiz is ...

  short marks + long marks = 70 +60 = 130 . . . available marks

And Keith's overall score was ...

  (Keith's short marks + Keith's long marks)/(available marks)

  = (50 +20)/130 = 70/130 . . . . Keith's score ratio for the quiz

Otras preguntas