A person’s Body Mass Index (BMI) is given by the following formula:
BMI = \( \frac{w}{h^2} \)
where \( w \) is their weight in kg, and \( h \) is their height in metres - Junior Cycle Mathematics - Question 1 - 2017
Question 1
A person’s Body Mass Index (BMI) is given by the following formula:
BMI = \( \frac{w}{h^2} \)
where \( w \) is their weight in kg, and \( h \) is their height in m... show full transcript
Worked Solution & Example Answer:A person’s Body Mass Index (BMI) is given by the following formula:
BMI = \( \frac{w}{h^2} \)
where \( w \) is their weight in kg, and \( h \) is their height in metres - Junior Cycle Mathematics - Question 1 - 2017
Step 1
Geri's BMI Calculation
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Answer
To calculate Geri's BMI, we use the formula:
BMI=h2w
Substituting in Geri's weight and height:
BMI=(1.63)277.5=2.656977.5≈29.2
Thus, Geri's BMI is 29.2.
Step 2
Geri's New Weight Calculation
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Answer
To find Geri's new weight after losing weight with a BMI of 24.0, we use the formula again:
w=BMI×h2
Substituting the new BMI and Geri's height:
w=24.0×(1.63)2=24.0×2.6569≈63.8 kg
Therefore, Geri's new weight is 63.8 kg.
Step 3
Comparison of Alex's and Jo's BMI
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Answer
Since Alex is 10 cm taller than Jo, let ( h_J ) be Jo's height in meters. Then Alex's height is ( h_A = h_J + 0.1 ) meters.
Both have the same weight ( w ). According to the BMI formula:
BMIJ=hJ2wBMIA=(hJ+0.1)2w
To compare their BMIs, we note that as height increases, the denominator increases, hence:
BMIA<BMIJ
Thus, Alex’s BMI is less than Jo’s.
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