Peter, Ned and Morris have some apples. Ned has 2 1/3 as many apples as Peter. Morris has half as many apples as Ned. In total they have 999 apples. How many does each person have?
First, we set each person to a variable.
If Peter=x, or (6/6)x
Ned=2 1/3 x, or (7/3)x, or (14/6)x,
Since the total number of apples was 999, (6/6)x+(14/6)x+(7/6)x=999
Adding the x coefficients together, we get (27/6)x=999.
To get rid of the fraction, multiply both sides by (6/27).
This results in x=999*(6/27)
If we plug this in for each person, we get
It is also helpful to make a graph (as shown below) for convenience:
|name||# of apples||value of apples||total # of apples|
(obviously the 3rd column would not be needed for this problem)