AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 12 Medium

The ratio of girls to boys participating in a math competition is 1 : 3. The overall average score of the competition is 82 points, and the average score of the boys is 80 points. What is the average score of the girls?

  • A.

    82

  • B.

    84

  • C.

    86

  • D.

    88

  • E.

    90

Answer:D

Assume the number of girls is 1 and the number of boys is 3, based on the given ratio.

Using the formula: \text{average score} = \frac{\text{total score}}{\text{total number of students}}

we can calculate the total score of all students and the total score of the boys.

Subtracting the boys' total score from the overall total score gives the girls' total score.

Dividing that by the number of girls gives the average score of the girls.

The key to solving this problem is using the relationship: \text{average} = \frac{\text{total score}}{\text{total number of students}}

First find the total score and the boys' total score.

Their difference is the girls' total score, and dividing by the number of girls gives the girls' average.

Assume there is 1 girl and 3 boys.

Total score: 82 \times (1 + 3) = 328 \quad \text{(points)}

Boys' total score: 80 \times 3 = 240 \quad \text{(points)}

Girls' average score: (328 - 240) \div 1 = 88 \quad \text{(points)}

Answer: The average score of the girls is 88 points.

So option \text{D} is correct.

Therefore, the answer is \text{D}.

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