To solve this problem, we can use the concept of weighted averages.

1. Let's denote the fraction of the children that are girls as 'g' and the fraction of the children that are boys as 'b'. Since these are fractions of a whole (the total group), we know that g + b = 1.

2. We also know that the average height of all the children in the group is a weighted average of the average heights of the girls and boys, with the weights being the fractions of the group that are girls and boys, respectively. This gives us the equation: 138 = 135g + 150b.

3. We can substitute b = 1 - g from the first equation into the second equation to get: 138 = 135g + 150(1 - g).

4. Simplifying this equation gives: 138 = 135g + 150 - 150g, which simplifies further to: 12 = 15g.

5. Solving for g gives: g = 12 / 15 = 0.8.

So, 80% or 4/5 of the children in the group are girls.

Question

To solve this problem, we can use the concept of weighted averages.

1. Let's denote the fraction of the children that are girls as 'g' and the fraction of the children that are boys as 'b'. Since these are fractions of a whole (the total group), we know that g + b = 1.

2. We also know that the average height of all the children in the group is a weighted average of the average heights of the girls and boys, with the weights being the fractions of the group that are girls and boys, respectively. This gives us the equation: 138 = 135g + 150b.

3. We can substitute b = 1 - g from the first equation into the second equation to get: 138 = 135g + 150(1 - g).

4. Simplifying this equation gives: 138 = 135g + 150 - 150g, which simplifies further to: 12 = 15g.

5. Solving for g gives: g = 12 / 15 = 0.8.

So, 80% or 4/5 of the children in the group are girls.

Knowee AI · Accepted Answer

To solve this problem, we can use the concept of weighted averages.

1. Let's denote the fraction of the children that are girls as 'g' and the fraction of the children that are boys as 'b'. Since these are fractions of a whole (the total group), we know that g + b = 1.

2. We also know that the average height of all the children in the group is a weighted average of the average heights of the girls and boys, with the weights being the fractions of the group that are girls and boys, respectively. This gives us the equation: 138 = 135g + 150b.

3. We can substitute b = 1 - g from the first equation into the second equation to get: 138 = 135g + 150(1 - g).

4. Simplifying this equation gives: 138 = 135g + 150 - 150g, which simplifies further to: 12 = 15g.

5. Solving for g gives: g = 12 / 15 = 0.8.

So, 80% or 4/5 of the children in the group are girls.

There are some girls and boys in a group. The average height of the girls is 135cm and the average height of the boys is 150cm. Given that the the average height of all the children in the group is 138cm, what fraction of the children are girls?

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