Question

Watermelon one is 2 kilograms lighter than watermelon two and its weight is one-fifth of the weight of watermelon three. Watermelons one and three together are 3 times as heavy as watermelon two. Find the weight of each watermelon.

A) Watermelon one = 4 kg, Watermelon two = 6 kg, Watermelon three = 8 kg
B) Watermelon one = 2 kg, Watermelon two = 4 kg, Watermelon three = 10 kg
C) Watermelon one = 5 kg, Watermelon two = 7 kg, Watermelon three = 15 kg
D) Watermelon one = 3 kg, Watermelon two = 5 kg, Watermelon three = 12 kg

Answer 1

By setting up a system of equations based on the given relationships between each watermelon's weight, solving these equations yields the weights of the watermelons as 2 kg for watermelon one, 4 kg for watermelon two, and 10 kg for watermelon three.

Step-by-step explanation:

To solve the problem of determining the weight of each watermelon, let's define the weights as follows:

• Watermelon one = W1
• Watermelon two = W2
• Watermelon three = W3

From the information given:

1. W1 is 2 kilograms lighter than W2, so W1 = W2 - 2 kg.
2. W1 is one-fifth the weight of W3, so W1 = W3 / 5.
3. Together, W1 and W3 weigh three times as much as W2, so W1 + W3 = 3W2.

Using the second equation, we can express W3 in terms of W1: W3 = 5W1.

Next, we substitute W3 in the third equation with 5W1:

W1 + (5W1) = 3W2

Solving this, we get:

6W1 = 3W2

Dividing both sides by 3:

2W1 = W2

Now, we substitute this relationship back into the first equation:

W1 = (2W1) - 2 kg ⇒ W1 - 2 kg = 2W1 - 2 kg ⇒ W1 = 2 kg

Then, we find W2:

W2 = 2W1 ⇒ W2 = 2 * 2 kg ⇒ W2 = 4 kg

Finally, we determine W3:

W3 = 5W1 ⇒ W3 = 5 * 2 kg ⇒ W3 = 10 kg

Therefore, the correct answer is:

• Watermelon one = 2 kg
• Watermelon two = 4 kg
• Watermelon three = 10 kg

Which corresponds to option B.