A total of 80 pupils take part in a mathematics test and the average score was 69 marks. Given the average score of the boys was 75 marks and the average score for the girls was 65 marks. find the number of boys who took the test.
b boys, 80-b girls
Now add up the total points scored:
75(b) + 65(80-b) = 69(80)
Fast method:
Ratio of boys to girls
= (69-65):(75-69)
=4:6
=2:3
Number of boys = 80*2/(2+3) = 32
Standard method:
Let x=number of boys
(75*x + 65*(80-x))/80 = 69
Solve for x
75x-65x = 69*80-5200 = 320
10x=320
x=32
Answer: there are 32 boys.
To find the number of boys who took the test, we need to use the given information about the average score of the boys and girls.
Let's assume that the number of boys who took the test is "x".
The average score of the boys is given as 75 marks, which means the total marks obtained by the boys will be 75x.
Now, let's find the number of girls who took the test. Since the total number of pupils who took the test is 80, we can subtract the number of boys from the total to get the number of girls. So the number of girls is 80 - x.
Next, we can calculate the total marks obtained by the girls. The average score for the girls is given as 65 marks, so the total marks obtained by the girls will be 65 times the number of girls, which is 65(80 - x).
We know that the average score for the entire group of pupils is 69 marks, so we can calculate the total marks obtained by the entire group. Since the number of boys and girls combined is 80, the total marks obtained by the group will be 69 multiplied by 80, which is 69(80).
Now, to find the number of boys who took the test, we can set up an equation based on the above calculations:
Total marks obtained by boys (75x) + Total marks obtained by girls (65(80 - x)) = Total marks obtained by entire group (69(80))
75x + 65(80 - x) = 69(80)
We can solve this equation to find the value of x, which will give us the number of boys who took the test.