Final answer:
To solve for the weights of the bags, we set up an equation and find that the weight of each of the lighter bags is 1 17/20 kg, and the weight of the heavier bag is 3 1/20 kg.
Step-by-step explanation:
The question asks us to calculate the weight of each bag of sweets when given the total weight and the additional weight of the heavier bag. Let's denote the weight of the two equal bags as 'x' kilograms each. According to the problem, the third bag weighs 'x + 1 1/5' kg, which is heavier by 1 1/5 kg than each of the other two bags. The total weight of the three bags is 6 3/4 kg.
Starting with this information, we can set up an equation to find the value of 'x': 2x + (x + 1 1/5 kg) = 6 3/4 kg. To solve for 'x', first simplify the right side of the equation by converting the mixed fraction to an improper fraction: 6 3/4 kg = 27/4 kg. Now, convert 1 1/5 kg to an improper fraction as well: 1 1/5 kg = 6/5 kg. The equation now is: 2x + x + 6/5 = 27/4 kg.
Combining like terms, we have: 3x = 27/4 kg - 6/5 kg. To combine these fractions, we need a common denominator, which would be 20 in this case. This changes the equation to: 3x = (27/4) * (5/5) - (6/5) * (4/4) = 135/20 kg - 24/20 kg = 111/20 kg. To find 'x', divide both sides by 3: x = (111/20 kg) / 3 = (111/20) * (1/3) kg = 37/20 kg = 1 17/20 kg. This is the weight of each of the lighter bags.
Subsequently, the weight of the heavier bag can be found by adding the additional weight: x + 6/5 kg = (37/20 kg) + (6/5 kg) = (37/20) + (24/20) = 61/20 kg = 3 1/20 kg.
Therefore, the weight of the two bags with equal weight is 1 17/20 kg each, and the weight of the heavier bag is 3 1/20 kg.