In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
Practice Questions
1 question
Q1
In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
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Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.
Questions & Step-by-step Solutions
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Q
Q: In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
Solution: Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.
Steps: 13
Step 1: Understand that there are 30 students in total in the class.
Step 2: Let 'x' be the number of boys in the class.
Step 3: Since there are 30 students, the number of girls will be '30 - x'.
Step 4: The average score of the boys is 80, so the total score of the boys is 80 times the number of boys, which is 80x.
Step 5: The average score of the girls is 70, so the total score of the girls is 70 times the number of girls, which is 70(30 - x).
Step 6: The overall average score of the class is 75, which means the total score of all students divided by the number of students (30) equals 75.
Step 7: Write the equation for the overall average: (80x + 70(30 - x)) / 30 = 75.
Step 8: Multiply both sides of the equation by 30 to eliminate the fraction: 80x + 70(30 - x) = 75 * 30.
