To determine the ratio of boys to girls in the class, we can use the information given about the average heights of boys, girls, and the class as a whole.
Let's denote \( x \) as the number of boys and \( y \) as the number of girls in the class. We want to find the ratio \( \frac{x}{y} \).
We are given the following average heights:
- Average height of boys, \( \text{boy\_avg\_height} = 165 \) cm,
- Average height of girls, \( \text{girl\_avg\_height} = 155 \) cm,
- Average height of the whole class, \( \text{class\_avg\_height} = 160 \) cm.
Using the formula for average height of the class, we can express the total height of all boys combined and all girls combined as:
\[ \text{boy\_avg\_height} \times x + \text{girl\_avg\_height} \times y = \text{class\_avg\_height} \times (x + y) \]
Substituting the values, we get:
\[ 165x + 155y = 160(x + y) \]
Now, expand the right side:
\[ 165x + 155y = 160x + 160y \]
Rearrange the equation to bring like terms together and solve for \( x \) in terms of \( y \):
\[ 165x - 160x = 160y - 155y \]
\[ 5x = 5y \]
Divide both sides by 5:
\[ x = y \]
Therefore, the ratio of the number of boys to girls \( \left( \frac{x}{y} \right) \) in the class is 1:1. This means there is an equal number of boys and girls in the class.
