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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?

 Dec 19, 2021
 #1
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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,

 Morris= (7/6)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)

999*(6/27)=222

If we plug this in for each person, we get

 

  Peter=222,

    Ned=518,

Morris=259

 

It is also helpful to make a graph (as shown below) for convenience:

name# of applesvalue of applestotal # of apples
Ned   
Morris   
Peter   

wink (obviously the 3rd column would not be needed for this problem)

 Dec 19, 2021
 #2
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Peter => x

 

x + 7x/3 + 1/2(7x/3) = 999

 

x = 222

 Dec 20, 2021

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