Expert: Sherry Wallin - 10/26/2010

Question
Hi Sherry, I have a word problem but I don't know if I'm correct.
A king took 1/6 of the apples from a pile
The Queen took 1/5 from the remaining apples.
The oldest Prince took 1/4 of the remaining apples.
The second prince took 1/3 of the remaining apples.
The youngest Price took 1/2 of the remaining apples
There were 3 apples left.
How many apples was there to start?

what I did was write an equation.
1/6x+1/5+1/4+1/3+1/2=3
I solved for x. x=2160

Is this correct? Am I on the right track?
Thank you very much.

Answer
Sabrina~

Let x = the number of apples, so the king did take (1/6)x [notice the use of parentheses). The number of remaining apples will be
x - (1/6)x = (5/6)x

Now when the queen drew (1/5) of the remaining apples, that is
(1/5)(5/6)x = (1/6)x. At this point the number of remaining apples is:
(5/6)x - (1/5)(5/6)x = (5/6)x  - (1/6)x = (4/6)x

When the oldest prince takes (1/4) of the remaining apples he is taking:

(1/4)(4/6)x = (1/6)x. The number of remaining apples is:
(4/6)x - (1/6)x = (3/6)x

And then the second prince took (1/3) of the remaining apples, that is
(1/3)(3/6)x = (1/6)x. Now the number of remaining apples ia:
(3/6)x - (1/6)x = (2/6)x

Finally the youngest prince takes (1/2) of the remaining apples:
(1/2)(2/6)x = (1/6)x, so the number of the remaining apples is
(2/6)x-(1/6)x = (1/6)x

You probably began to see the pattern a bit back but now you know that
(1/6)x = 3 or that x = 18. Check and see if it fits the problem:

(1/6)(18) = 3 apples the king took
(1/5)(18-3) = (1/5)(15) = 3 apples the queen took
(1/4)(15-3) = (1/4)(12) = 3 apples the oldest prince took
(1/3)(12-3) = (1/3)(9) = 3 apples the second prince took
(1/2)(9-3) = (1/2)(6) = 3 apples the youngest prince took
the number of apples left is 6-3 = 3. It works!

Math Prof