To solve the problems where \( A \) and \( B \) have a relationship given by \( A = \frac{1}{7}B + 8 \) (assuming that's the equation you intended to present), let's break this down into the two parts.
Part 1: Finding \( A \) when \( B = 0.4 \)
Using the equation: \[ A = \frac{1}{7}B + 8 \]
Substituting \( B = 0.4 \): \[ A = \frac{1}{7}(0.4) + 8 \] \[ A = \frac{0.4}{7} + 8 \approx 0.0571 + 8 \approx 8.0571 \]
So, when \( B = 0.4 \), \( A \approx 8.0571 \).
Part 2: Finding \( B \) when \( A = 7.5 \)
Using the same equation: \[ 7.5 = \frac{1}{7}B + 8 \]
To isolate \( B \), we first subtract 8 from both sides: \[ 7.5 - 8 = \frac{1}{7}B \] \[ -0.5 = \frac{1}{7}B \]
Now, multiplying both sides by 7: \[ B = -0.5 \times 7 = -3.5 \]
So, when \( A = 7.5 \), \( B = -3.5 \).
Summary of Results
- When \( B = 0.4 \), \( A \approx 8.0571 \).
- When \( A = 7.5 \), \( B = -3.5 \).