Formula A: `BMI=w/h^2`
Formula B: `BMI=(4w-100)/5`
The formulas above are used in nutrition to estimate the body mass index BMI, in kilograms per square meter, of adults whose weight w ranges between 50 and 100 kilograms and whose height h is measured in meters.
Based on formula B, what is w in terms of BMI?
Based on Formula B, what is w in terms in BMI?

Options

A. `w=5BMI+25`
B. `w=5BMI-25`
C. `w=(5BMI+100)/4`
D. `w=(5BMI-100)/4`

Answer

To find \( w \) in terms of \( BMI \) based on Formula B, we start with the equation given by Formula B:

\[ BMI = \frac{4w - 100}{5} \]

### Step 1: Cross Multiply
To eliminate the fraction, we can cross-multiply. This gives us:

\[ 5 \cdot BMI = 4w - 100 \]

### Step 2: Rearrange the Equation
Next, we want to isolate \( w \). We can rearrange the equation by adding 100 to both sides:

\[ 5 \cdot BMI + 100 = 4w \]

### Step 3: Solve for \( w \)
Now, we divide both sides by 4 to solve for \( w \):

\[ w = \frac{5 \cdot BMI + 100}{4} \]

Thus, we have expressed \( w \) in terms of \( BMI \):

\[ w = \frac{5 \cdot BMI + 100}{4} \]

### Final Answer
The final expression for \( w \) in terms of \( BMI \) is:

\[ w = \frac{5 \cdot BMI + 100}{4} \]

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