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Answer :
To solve this problem, we need to find out how much the empty bottle weighs. Here’s a step-by-step approach:
1. Identify the total weight when the bottle is full:
The bottle with all the liquid in it weighs 420 grams.
2. Identify the total weight when half of the liquid is removed:
When half of the liquid is removed, the weight is 230 grams.
3. Determine the weight of the liquid removed:
The difference in weight when the bottle is full and when it is half-full is:
[tex]\[
420 \, \text{grams (full)} - 230 \, \text{grams (half-full)} = 190 \, \text{grams}
\][/tex]
Half of the liquid weighs 190 grams.
4. Calculate the total weight of the liquid:
Since 190 grams is half of the liquid, the total weight of all the liquid when the bottle is full is double that:
[tex]\[
190 \, \text{grams} \times 2 = 380 \, \text{grams}
\][/tex]
5. Determine the weight of the empty bottle:
To find just the weight of the bottle, subtract the weight of the total liquid from the full weight:
[tex]\[
420 \, \text{grams (full weight)} - 380 \, \text{grams (liquid)} = 40 \, \text{grams}
\][/tex]
Therefore, the bottle itself weighs 40 grams. The correct answer is H. 40.
1. Identify the total weight when the bottle is full:
The bottle with all the liquid in it weighs 420 grams.
2. Identify the total weight when half of the liquid is removed:
When half of the liquid is removed, the weight is 230 grams.
3. Determine the weight of the liquid removed:
The difference in weight when the bottle is full and when it is half-full is:
[tex]\[
420 \, \text{grams (full)} - 230 \, \text{grams (half-full)} = 190 \, \text{grams}
\][/tex]
Half of the liquid weighs 190 grams.
4. Calculate the total weight of the liquid:
Since 190 grams is half of the liquid, the total weight of all the liquid when the bottle is full is double that:
[tex]\[
190 \, \text{grams} \times 2 = 380 \, \text{grams}
\][/tex]
5. Determine the weight of the empty bottle:
To find just the weight of the bottle, subtract the weight of the total liquid from the full weight:
[tex]\[
420 \, \text{grams (full weight)} - 380 \, \text{grams (liquid)} = 40 \, \text{grams}
\][/tex]
Therefore, the bottle itself weighs 40 grams. The correct answer is H. 40.
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