A basket containing 80 eggs weighs 2kg 300g. The same basket containing 60 eggs weighs 1kg 700g. Find the mass of the empty basket.
1 kg = 1000 g
2 kg 300 g = 1 kg + 1 kg + 300 g = 1 kg + 1000 g + 300 g = 1 kg 1300 g
2 kg 300 g - 1 kg 700 g = 1 kg 1300 g - 1 kg 700 g = 600 g
The mass of the empty basket = 600 g
To find the mass of the empty basket, we need to determine the weight of the eggs in the basket and then subtract that weight from the total weight of the basket.
Let's start by calculating the weight of the eggs in the basket with 80 eggs. We know that the weight of the basket with the eggs is 2kg 300g. To find the weight of the eggs, we subtract the weight of the empty basket (which we are trying to find) from the total weight.
Let's represent the weight of the empty basket as "x" kilograms.
Weight of eggs in the basket with 80 eggs = Total weight of the basket with eggs - Weight of the empty basket
= 2kg 300g - x kg
Now, we need to do the same calculation for the basket with 60 eggs. The weight of the basket with 60 eggs is 1kg 700g. Again, we will subtract the weight of the empty basket from the total weight to find the weight of the eggs.
Weight of eggs in the basket with 60 eggs = Total weight of the basket with eggs - Weight of the empty basket
= 1kg 700g - x kg
Now, we have two equations representing the weight of the eggs in each basket:
1) 2kg 300g - x kg (weight of eggs in the basket with 80 eggs)
2) 1kg 700g - x kg (weight of eggs in the basket with 60 eggs)
Since the number of eggs is different in each basket, the weight of the eggs will be proportional to the number of eggs. We can set up a proportion to solve for x (the weight of the empty basket).
(weight of eggs in the basket with 80 eggs) / 80 = (weight of eggs in the basket with 60 eggs) / 60
(2kg 300g - x kg) / 80 = (1kg 700g - x kg) / 60
To simplify the calculation, let's convert the weights to a single unit. We can convert kg and grams to grams.
2kg 300g = 2300g
1kg 700g = 1700g
(2300g - x) / 80 = (1700g - x) / 60
To eliminate the fractions, we can cross-multiply:
60(2300g - x) = 80(1700g - x)
138,000g - 60x = 136,000g - 80x
138,000g - 136,000g = -20x + 60x
2,000g = 40x
Divide both sides by 40:
50g = x
Therefore, the weight of the empty basket is 50 grams.