Height is really mean

Algebra Level 1

if the mean height of boys in class is 60 centimetres,the mean height of girls is 55 centimetres and the mean height of all the students in the class is 57 cm, what will be the ratio of the number of boys to the number of girls?

2:5 2:3 1:1 3:4

Manish Mayank by Manish Mayank , 20, India

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1 solution

The average height of all the students can be derived from the average heights of each gender (or sex, whichever you prefer) by adding the average height multiplied to the number of people constituting that average. Therefore, assuming the total of students that are boys is x and the total number of students that are girls is y, we get

60 x + 55 y x + y = 57 \frac{60x + 55y}{x + y} = 57 60 x + 55 y = 57 ( x + y ) 60x + 55y = 57(x + y) 60 x + 55 y = 57 x + 57 y 60x + 55y = 57x + 57y 60 x − 57 x = 57 y − 55 y 60x - 57x = 57y - 55y 3 x = 2 y 3x = 2y 3 x 3 y = 2 y 3 y \frac{3x}{3y} = \frac{2y}{3y} x y = 2 3 \frac{x}{y} = \frac{2}{3}

And, thus, we can conclude that x:y is 2:3.

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