Question

In a store window, there was a flat containing boxes of berries having a total weight of $200$ kg. An analysis showed that the berries were $99\%$ moisture, by weight. After two days in the sun, a second analysis showed that the moisture content of the berries was only $98\%$, by weight. What was the total weight of the berries after two days, in kg?

Answer 1

100 kilograms!!!!

Explanation:

First of all, let's find the variable and what it should represent.

Let's say m stands for the moisture in the berries.

Since the berries are 200 kg and the moisture in the berries is 99%, which is 198 kg. 2 kg remain, so we the left part of our equation will be :

m/(m+2).

The right part of our equation will be 0.98 because 0.98 is 98%, which is m.

m/(m+2)=0.98.

When we multiply m+2 on both sides, we get:

m=0.98m+1.96.

Subtracting 0.98m on both sides gives us 0.02m=1.96.

Dividing 0.02 on both sides gives us:

m=98.

The question is asking what is the total weight of the berries after two days, so we add 2 to 98, or 2+m, which is 100.

100 kilograms is the answer.

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Answer 2

100 kg

Explanation:

Data provided in the question:

Initial total weight of the berries = 200 kg

Initial weight of water present = 99% of the weight

= 198 kg

therefore,

Initial weight of the solids in berries = 200 kg - 198 kg = 2 kg

After 2 days water was 98% of the total weight of the berries

Thus,

2% was solid which means 2 kg was 2% of the total weight of the berries

Thus,

2% of Total weight of berries after two days = 2 kg

or

0.02 × Total weight of berries after two days = 2 kg

or

Total weight of berries after two days = [ 2 ÷ 0.02 ] kg

or

Total weight of berries after two days = 100 kg