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Answer :
Sure! Let's go through the solution step by step.
a) Calculate the percentage increase in weight:
1. Determine the initial and current weight:
- Last year's weight: [tex]\( 30 \, \text{kg} \)[/tex]
- Current weight: [tex]\( 36 \, \text{kg} \)[/tex]
2. Calculate the increase in weight:
[tex]\[
\text{Increase in weight} = 36 \, \text{kg} - 30 \, \text{kg} = 6 \, \text{kg}
\][/tex]
3. Calculate the percentage increase in weight:
[tex]\[
\text{Percentage increase} = \left( \frac{\text{Increase in weight}}{\text{Last year's weight}} \right) \times 100
\][/tex]
[tex]\[
\text{Percentage increase} = \left( \frac{6}{30} \right) \times 100 = 20\%
\][/tex]
So, the penguin's weight increased by 20%.
b) Calculate how tall the penguin was last year:
1. Determine the current height and the percentage increase:
- Current height: [tex]\( 135 \, \text{cm} \)[/tex]
- The percentage increase in height: [tex]\( 12.5\% \)[/tex]
2. Calculate last year's height:
Since the penguin is now [tex]\( 12.5\% \)[/tex] taller, you can find last year's height by dividing the current height by [tex]\( 1 + 0.125 \)[/tex]:
[tex]\[
\text{Last year's height} = \frac{\text{Current height}}{1 + \frac{12.5}{100}}
\][/tex]
[tex]\[
\text{Last year's height} = \frac{135}{1.125} = 120 \, \text{cm}
\][/tex]
Therefore, last year the penguin was 120 cm tall.
a) Calculate the percentage increase in weight:
1. Determine the initial and current weight:
- Last year's weight: [tex]\( 30 \, \text{kg} \)[/tex]
- Current weight: [tex]\( 36 \, \text{kg} \)[/tex]
2. Calculate the increase in weight:
[tex]\[
\text{Increase in weight} = 36 \, \text{kg} - 30 \, \text{kg} = 6 \, \text{kg}
\][/tex]
3. Calculate the percentage increase in weight:
[tex]\[
\text{Percentage increase} = \left( \frac{\text{Increase in weight}}{\text{Last year's weight}} \right) \times 100
\][/tex]
[tex]\[
\text{Percentage increase} = \left( \frac{6}{30} \right) \times 100 = 20\%
\][/tex]
So, the penguin's weight increased by 20%.
b) Calculate how tall the penguin was last year:
1. Determine the current height and the percentage increase:
- Current height: [tex]\( 135 \, \text{cm} \)[/tex]
- The percentage increase in height: [tex]\( 12.5\% \)[/tex]
2. Calculate last year's height:
Since the penguin is now [tex]\( 12.5\% \)[/tex] taller, you can find last year's height by dividing the current height by [tex]\( 1 + 0.125 \)[/tex]:
[tex]\[
\text{Last year's height} = \frac{\text{Current height}}{1 + \frac{12.5}{100}}
\][/tex]
[tex]\[
\text{Last year's height} = \frac{135}{1.125} = 120 \, \text{cm}
\][/tex]
Therefore, last year the penguin was 120 cm tall.
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