SOLUTION: I need not only answer,but solution too: A team of six girls, whose average height was 1.50m, realised that if they stood in order of height, each one was 2cm taller than the next

Question 831103: I need not only answer,but solution too:
A team of six girls, whose average height was 1.50m, realised that if they stood in order of height, each one was 2cm taller than the next. When a seventh girl joined them, the team�s average height increased by 1%. Find a) the height of the shortest girl and b) the height of the girl who joined the team last.
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
Let's work in cm only. And let A be the tallest girl, and so forth.
Here's what the question tells you:
(A + B + C + D + E + F)/6 = 150
B = A-2
C = A-4
D = A-6
E = A-8
F = A-10
We can substitute these values into the original equation
[A + (A-2) + (A-4) + (A-6) + (A-8) + (A-10)]/6 = 150
Multiply by 6 to get rid of that pesky fraction
[A + (A-2) + (A-4) + (A-6) + (A-8) + (A-10)] = 900
Add the As
6A -2 -4 -6 -8 -10 = 900
Add the numbers
6A -30 = 900
Add 30 to each side
6A = 930
Divide each side by 6
A = 155
.
The tallest girl is 155cm. Therefore, the other original girls are 153, 151, 149, 147, 145 <<--shortest girl.
.
6 girls * 150 = 900
.
But the girls' height increased by 1% when girl 7 joined.
[7 girls * 151.5 (1% increase of 150)]/7 = G (height of 7th girl)
1060.5 / 7 = 151.5 <<--new girl

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