16. Each day, Jack's donut shop starts with 100 donuts. Throughout the day, some donuts are sold, some are discarded, and some more is made according to the following principle: for every three donuts sold, one more is made. If on a particular day, Jack sold \( m \) donuts and discarded \( d \) donuts, and at the end of the day had no donuts left, which of the following gives the correct relation between \( m \) and \( d \) ? A. \( 2 m+3 d=300 \) B. \( 3 m+2 d=300 \) C. \( 3 d-2 m=300 \) D. \( 2 d-3 m=100 \) E. \( m+d=100 \)

To solve the problem, we need to establish the relationship between the number of donuts sold (\( m \)), the number of donuts discarded (\( d \)), and the number of donuts made throughout the day. 1. **Initial Count of Donuts**: Jack starts with 100 donuts. 2. **Donuts Sold**: Jack sells \( m \) donuts. 3. **Donuts Discarded**: Jack discards \( d \) donuts. 4. **Donuts Made**: For every 3 donuts sold, 1 donut is made. Therefore, if \( m \) donuts are sold, the number of donuts made is \( \frac{m}{3} \). Now, we can set up the equation for the total number of donuts at the end of the day: \[ \text{Initial donuts} - \text{Sold donuts} - \text{Discarded donuts} + \text{Made donuts} = 0 \] Substituting the values we have: \[ 100 - m - d + \frac{m}{3} = 0 \] To eliminate the fraction, we can multiply the entire equation by 3: \[ 3(100) - 3m - 3d + m = 0 \] This simplifies to: \[ 300 - 2m - 3d = 0 \] Rearranging gives us: \[ 2m + 3d = 300 \] Thus, the correct relation between \( m \) and \( d \) is: \[ \boxed{A. \, 2m + 3d = 300} \]