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In a class of 45 boys, the average height of the boys is 170 cm and the average height of the girls is 160 cm. If the average height of the class is more than 164 cm, find the maximum number of girls in the class.

Question

In a class of 45 boys, the average height of the boys is 170 cm and the average height of the girls is 160 cm. If the average height of the class is more than 164 cm, find the maximum number of girls in the class.

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Solution

To solve this problem, we need to set up an inequality based on the information given.

Let's denote the number of girls in the class as 'g'.

We know that the average height of the class is more than 164 cm. The average height is calculated by dividing the total height by the total number of students.

So, we can set up the following inequality:

(45170 + g160) / (45 + g) > 164

This simplifies to:

7650 + 160g > 164(45 + g)

Further simplifying, we get:

7650 + 160g > 7380 + 164g

Rearranging the terms, we get:

4g < 270

Finally, solving for 'g', we get:

g < 67.5

Since the number of girls must be a whole number, we round down to the nearest whole number.

So, the maximum number of girls in the class is 67.

This problem has been solved

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