SOLUTION: Hi A group of girls had an average height of 155cm.3 more girls joined the group and the average height became 157cm. If the 3 girls had the same height of 163cm each, how many gi

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Question 1207614: Hi
A group of girls had an average height of 155cm.3 more girls joined the group and the average height became 157cm. If the 3 girls had the same height of 163cm each, how many girls were there at first.
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
A group of girls had an average height of 155cm. 3 more girls joined the group
and the average height became 157cm. If the 3 girls had the same height of 163cm each,
how many girls were there at first.
~~~~~~~~~~~~~~~~~~~ 

Let n girls there were at first.


Then an equation to find n is

    %28155n+%2B+3%2A163%29%2F%28n%2B3%29 = 157.


Simplify and find n

    155n + 3*163 = 157*(n+3)

    155n + 489 = 157n + 471

    489 - 471 = 157n - 155n

        18    =     2n

         n    =     18/2 = 9.


ANSWER.  n = 9.   At first, there were 9 girls.

Solved.

--------------------

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Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The response from tutor @ikleyn shows a standard formal solution using the definition of average.

When the problem is about averages and the numbers are very close together, a quick informal solution can be obtained by comparing the individual numbers to the average.

In this problem, the 3 girls who joined the group each had a height of 163cm, which is 6cm above the new average of 157cm. That makes a total of 3*6cm = 18cm over the new average.

That means the heights of the original group of girls must be a total of 18cm under that new average. Since the average height of the girls in the original group was 2cm under the new average, the number of girls in the original group was 18/2 = 9.

ANSWER: 9

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
A group of girls had an average height of 155cm.3 more girls joined the group and the average height became 157cm. If the 3 girls had the same height of 163cm each, how many girls were there at first.

Let original number of girls be G
Then height of original number of girls = 155G
After another 3 joined the group, height of the entire group was, 155G + 3(163) = 155G + 489
Number in group after 3 more joined: G + 3
We then get: 
                                           155G + 489 = 157(G + 3) ----- Cross-multiplying
                                           155G + 489 = 157G + 471
                                          155G - 157G = 471 - 489
                                                 - 2G = - 18
                Original number of girls, or