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5. A pot full of water weighs 9.5 kg. When half-filled with water, the pot weighs 5.5 kg. What is the weight of the empty pot?

A. 4 kg
B. 1.5 kg
C. 2 kg
D. 3.5 kg

Sagot :

GinnyAnsweridn
To determine the weight of the empty pot, we need to set up a system of equations based on the given information:

1. Let [tex]\( W \)[/tex] represent the weight of the pot when empty.
2. Let [tex]\( w \)[/tex] represent the weight of the water when the pot is full.

### Step 1: Set Up Equations

When the pot is half-filled with water, the total weight is 5.5 kg. This can be written as:
[tex]\[ W + 0.5w = 5.5 \][/tex]

When the pot is completely filled with water, the total weight is 9.5 kg. This can be written as:
[tex]\[ W + w = 9.5 \][/tex]

### Step 2: Solve for [tex]\( w \)[/tex] and [tex]\( W \)[/tex]
First, we can subtract the first equation from the second equation to eliminate [tex]\( W \)[/tex]:

[tex]\[ (W + w) - (W + 0.5w) = 9.5 - 5.5 \][/tex]
[tex]\[ w - 0.5w = 4 \][/tex]
[tex]\[ 0.5w = 4 \][/tex]
[tex]\[ w = 8 \][/tex]

So, the weight of the water when the pot is full is 8 kg.

### Step 3: Substitute [tex]\( w \)[/tex] back into the First Equation

Now, we substitute [tex]\( w = 8 \)[/tex] back into the first equation:

[tex]\[ W + 0.5w = 5.5 \][/tex]
[tex]\[ W + 0.5 \times 8 = 5.5 \][/tex]
[tex]\[ W + 4 = 5.5 \][/tex]
[tex]\[ W = 5.5 - 4 \][/tex]
[tex]\[ W = 1.5 \][/tex]

Therefore, the weight of the empty pot is 1.5 kg.

### Conclusion
The weight of the empty pot is 1.5 kg. So, the correct answer is:

b. 1.5
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