# What is the weight of the empty box in the following case:A box contains an unknown number of apples. The total weight of the box and the apples is 200 kg. After 3/4 of the apples are removed the...

What is the weight of the empty box in the following case:

A box contains an unknown number of apples. The total weight of the box and the apples is 200 kg. After 3/4 of the apples are removed the box and the apples weigh 64 kg.

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Let us denote the weight of the box by B and the weight of the apples by A. Now initially we have A + B = 200, After 3/4 of the apples have been removed, we have the weight of the box and the apples as 64. This can be written as B + A / 4 = 64.

Now from the first equation A + B = 200, write A in terms of B as A = 200 – B.

Substitute this in B + A/4 = 64

=> B + (200 – B)/4 = 64

=> B + 200 / 4 – B/4 = 64

=> 3B/4 = 64 – 50

=> 3B/4 = 14

=> B = (14*4)/3

=> B = 56/ 3

**Therefore the empty box weighs 56/3 kg.**

Let the weight of the box be b and the weight of the apples be a.

Then the weight of the box with apples is 200 kg.

=> b+a = 200.....(1).

After 3/4 of the apples are removed the remaining apples have to weigh a/4 . The box with remaining apples should weigh b+a/4 and this is 64 kg.

=> b+a/4 = 64....(2)

(1)-(2): (b+a)-(b+a/4) = 200-64 = 136.

3a/4 = 136.

a = 136*4/3 = 6/3 = 544/3 = 181 1/3 kg.

We substitute a = 181 1/3 in (2): b+ (544)/3*4 = 64.

b = 64 - 544/12 = 64 - 136/3 = 45 1/3.

Therefore b = 45 1/3.

Therefore the weight of the empty box is 45 1/3 kg.