A certain number of apples are kept in five boxes; Box 1, Box 2, Box 3, Box 4, Box 5 such that:

(i) The number of apples in Box 3 is one-sixth of the total apples in Box 5.
(ii) Box 2 has twice as many apples as Boxes 3 and 5 combined.
(iii) Box 1 has half as many apples as Box 5
(iv)Box 4 has 10 more apples than Box 1.
(v) Box 4 has 1/4 as many apples as Box 2.

Determine which boxes contain how many apples and the total number of apples in all the five boxes.

First label the boxes A-E instead of 1-5. Then:

By statement 1: E = 6C
By statement 2: B = 2(C+E) = 14C
By statement 3: A = E/2 = 3C
By statement 4: D = A + 10 = 3C + 10
By statement 5: D = B/4 = 7C/2

Combining statements 4 and 5:

7C/2 = 3C + 10
C/2 = 10
C = 20

So the contents of the boxes are:

A = 60
B = 280
C = 20
D = 70
E = 120

For a grand total of 550 apples. Hopefully zero worms...

Posted by Jyqm on 2007-02-20 09:01:03