1/7:30=2,5d:4

To solve the equation \( \frac{1}{7:30} = \frac{2.5d}{4} \), we first interpret the ratio \( 7:30 \). 1. Convert the ratio \( 7:30 \) into a fraction. This gives us: \[ 7:30 = \frac{7}{30} \] 2. Next, we rewrite the left side of the equation: \[ \frac{1}{\frac{7}{30}} = \frac{30}{7} \] So now we have: \[ \frac{30}{7} = \frac{2.5d}{4} \] 3. To eliminate the fraction on the right side, multiply both sides by 4: \[ 4 \times \frac{30}{7} = 2.5d \] This simplifies to: \[ \frac{120}{7} = 2.5d \] 4. Now, isolate \( d \) by dividing both sides by \( 2.5 \): \[ d = \frac{120/7}{2.5} \] 5. To simplify \( \frac{120/7}{2.5} \), note that \( 2.5 = \frac{25}{10} = \frac{5}{2} \): \[ d = \frac{120}{7} \cdot \frac{2}{5} = \frac{240}{35} = \frac{48}{7} \] Therefore, the solution for \( d \) is: \[ d = \frac{48}{7} \approx 6.857 \] If you have any further questions or need clarification, feel free to ask!