   SEARCH HOME Math Central Quandaries & Queries  Question from Isaac: The average mass of a group of children is 50 kilograms. Todd, who has a mass of 62 kilograms, then joins the group. This raises the average mass of the group to 52 kilograms. How many children were in the original group Hi Isaac,

If you had the data from the children then you would know the total mass and the number of children so you could calculate the average mass. Since you don't know the total mass or the number of students assign letters to these quantities.

Let the total mass of the students be $T$ kilograms and the number of students be $n.$ What would you do with $t$ ad $n$ to calculate the average mass? The result would be 50 kilograms so this gives you an equation in $T$ and $n.$

Now Todd arrives and his data is added to the data from the others. What is the total mass now? What is the number of students? What would you do to calculate the average mass now? The result this time is 52 kilograms. This gives you a second equation is $T$ and $n.$

Solve the two equations for $n.$

Now that you know $n$ it's an easy calculation to find $T.$ With $n$ and $T$ known you can verify that your answer is correct.

Write back if you need further assistance,

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.