average height of 25 boys in a class is 150 cms and the average height of 22 girls is 145 cms. if the height of three teachers are added the average height of all the students and the teachers becomes 148.4 cms. among the teachers maximum height is 165 cms and the minimum height is 157 cms.what is the height of the third teacher?
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Answer:
158 cm
Step-by-step explanation:
Let t be the height of the third teacher, so their heights are 165 cm, 157 cm and t.
The sum of the heights of all the boys is: 25 × 150 cm = 3750 cm
The sum of the heights of all the girls is: 22 × 145 cm = 3190 cm
Strategy: There are two ways to get the sum of everyone's heights: via the average which is given, and by adding the heights which includes t. This gives an equation for t that we can solve.
The sum of all 25+22+3 = 50 people's heights is:
3750 cm + 3190 cm + 165 cm + 157 cm + t = t + 7262 cm.
Since the average is 148.4 cm, the sum of all 50 people's heights is also
50 × 148.4 cm = 7420 cm.
Therefore
t + 7262 cm = 7420 cm
=> t = 7420 cm - 7262 cm = 158 cm.
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