Principal Nigel's Math Question

We know that, since the ratio of girls to boys is 7:6, the total number of girls must be a multiple of 7, the total number of boys must be a multiple of 6 and hence the total number of pupils must be a multiple of 13. Let us assume that the class is the smallest possible (with 13 members, 7 girls, 6 boys). The average height of the girls is 54 inches, so 7 x 54 inches (378 inches) is all of the added heights of the girls in the class. The average height of the boys is 55 inches, so 6 x 55 inches (330 inches) is all of the added heights of the girls in the class. The total height therefore of the entire class is 378 + 330, 708 inches. This, divided by the total number of students in the class (13), will give the class average. 708 ÷ 13 = 54.46 (to 2 decimal places or 4 significant figures). So 54.46 inches is the class average.

total=13 [(7x54) + (6x55)] /13 = 54.46

This is just a generalization of Freddie's answer:

To generalize we can just include a variable.

Since we know the number of girls is a multiple of 7 and the number of boys must be the same multiple of 6.

We can express the number of girls as 7n and boys as 6n.

Total height of girls: 54*7n = 378n

Total height of boys: 55*6n = 330n

Total height of all students: 378n+330n = 708n

Total number of students: 7n + 6n = 13n

Average of all students 708n/13n

Approximately 54.46153846153846

So: 54.46 in

Hello,

let x = the average height of those studens,

x = (54 x 7) + ( 55 x 6) / (7 + 6)

x = 708 / 13

x = 54.46 inches...

thanks....

We can short cut this solution with simple elimination (or we can do the math). Max height is 55 min height is 54 so the solution must fall in that range, eliminating 56.26 and 52.28. Since there are more girls than boys in the class the solution must be closer to 54 than to 55 so the only remaining solution that fits is 54.46.

No more arguments, the answer is 54.46, said SHERLOCK HOLMES

suppose, number of girls=G number of boys=B

average of girls height=sum of girls height/G=54 sum of girls height=54 G .............(1)

as same for boys we get sum of boys height=55 B ............(2)

As given in problem G/B=7/6 G=7/6 B so average of all students = sum of girls height+sum of boys height/(G+B) =54 G+55 B/(7/6 B+B) =118 B*6/13 B =54.46

CAN BE DONE BY:

54 +55= 109

Average= 109/2 = 54.5. but ans is 54.46. If we reduce this 6 to 4 then 4 becomes 5, and there you go you just have the ans 54.5

The answer is 54.46.