SOLUTION: Hi the average mass of a group of people was 42kg at first. When one person weight 70kg joined the average mass became 46kg. How man people were in the group at first. thanks

Question 1149800: Hi
the average mass of a group of people was 42kg at first. When one person weight 70kg joined the average mass became 46kg. How man people were in the group at first.
thanks
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52806)   (Show Source): You can put this solution on YOUR website!
.

Let the number under the question is "n". Then the total mass of "n" people is 42*n kilograms. When the 70-kilo person was added to the group, the mass became (42*n+70) kilograms; the number of people in the extended group is (n+1) now. So your equation is = 46. To solve the equation, first multiply both sides by (n+1). You will get 42*n + 70 = 46*(n+1). The rest is clear, and I leave it to you to complete the solution on your own.

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Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let x = the total value
let n = the number of elements that make up the total.

the average mass at first was 42.
formula for that is x/n = 42

additional person weighing 70 kg is added to the group.
the average mass becomes 46.
formula for that is (x+70)/(n+1) = 46

solve for x in the first equation to get x = 42*n
replace x in the second equation to get (42*n+70)/(n+1) = 46
multiply both sides of this equation by (n+1) to get:
(42*n+70) = 46*(n+1)
simplify to get 42*n+70 = 46*n+46
subtract 42*n from both sides of the equation and subtract 46 from both sides of the equation to get:
70-46 = 46*n-42*n
simplify to get:
24 = 4*n
solve for n to get n = 6

x/n = 42 becomes x/6 = 42
solve for x to get x = 252

(x+70)/(n+1) = 46 becomes (252+70)/(6+1) = 46 which becomes 322/7 = 46 which becomes 46 = 46 which is true.

your solution is that there were 6 people in the group at first.

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