SOLUTION: 1. The average mass of some children in a group was 36kg. When one child who weighed 54kg left the group, the average mass of the remaining children decreased by 2kg. How many chil

Algebra ->  Average -> SOLUTION: 1. The average mass of some children in a group was 36kg. When one child who weighed 54kg left the group, the average mass of the remaining children decreased by 2kg. How many chil      Log On


   

Question 916155: 1. The average mass of some children in a group was 36kg. When one child who weighed 54kg left the group, the average mass of the remaining children decreased by 2kg. How many children were there in the group at first?
Teacher's working:
54kg-36kg=24kg
18kg divided by 2= 9kg
2. A group of pupils calculated their average score for a science test. They noted that if anyone scored 14 marks more, their average score would be 90. If anyone scored 4 marks fewer, their average score would be 88. How many pupils are there in the group?
Teacher's working:
14+4=18
18 divided by 2 =9
I don't understand why in the first question we minus and the second question plus. Can you explain both the questions? Please answer by today because tomorrow is my maths exam!!! Make the solution easy cause I'm still in P5!!
Found 2 solutions by rothauserc, ewatrrr:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1)let x be the total mass of the group, then
x / n = 36, where n is the number of students
when one child weighing 54kg leaves the group we have
(x-54) / (n-1) = 36 - 2 = 34
we have two equations
x = 36n
x-54 = 34(n-1)
x-54 = 34n -34
substitute for x in second equation
36n -54 = 34n -34
subtract 34n from both sides of =
add 54 to both sides of =
2n = 20
n = 10
there are 10 students
2) let x be the sum of their scores and y be the average, then
x / n = y where n is the number of students, also we are given
(x+14) / n = 90
(x-4) / n = 88
from first equation
x = 90n - 14
substitute in second equation
90n - 14 -4 = 88n
subtract 88n from both sides of =
2n -18 = 0
2n = 18
n = 9


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
1. 36n the total weight of group originally (concept of average weight)
%2836n+-+54%29%2F%28n-1%29 = 34 (one weighing 54kg left group)
36n - 54 = 34n - 34
2n = 20
n = 10 children were there in the group at first. Then 9 when one left.
......
2. T being the total of all scores originally
%28T+%2B+14%29%2Fn+=+90 concept of Average score
T + 14 = 90n
%28T+-4%29%2Fn+=+88 concept of Average score
T - 4 = 88n
Finding n...
T+14 = 90n
-(T-4 = 88n)
18 = 2n
9 = n