Question

One parcel weighs x kg and another is three times as heavy. If 2kg is added to the heavier parcel and 8kg to the lighter parcel they will be of equal weight. Find the weight of each.

Answer 1

After writing and solving the equation x + 8 = 3x + 2 for the two parcels, we find that the lighter parcel weighs 3 kg and the heavier parcel weighs 9 kg. When the specified weights are added to each, both parcels end up weighing 11 kg.

Step-by-step explanation:

One parcel weighs x kg and another is three times as heavy. To solve for the weight of each parcel when they are said to be equal after adding 2kg to the heavier and 8kg to the lighter, we set up the following equation: x + 8 = 3x + 2.

First, we bring all the x terms on one side and the numerical values on the other side of the equation:

• x - 3x = 2 - 8
• -2x = -6

Now we divide both sides by -2 to solve for x:

• x = 3 kg

The weight of the lighter parcel is thus 3 kg. Consequently, the heavier parcel, being three times heavier, weighs 9 kg.

When we add the specified weights, we have:

• Lighter parcel + 8kg = 3kg + 8kg = 11kg
• Heavier parcel + 2kg = 9kg + 2kg = 11kg

Both parcels now weigh 11 kg, confirming our solution.