A shipment of 10 tons of sugar is separated into containers of equal size. If the shipment fills \( 3 \frac{3}{4} \) containers, how much sugar can one container hold? Write your answer as a mixed number in simplest form.

To find out how much sugar one container can hold, we first need to convert the total weight of the shipment into a single number. The shipment is 10 tons of sugar, which is equivalent to \( 10 \) tons or \( 10 \) as a fraction. The shipment fills \( 3 \frac{3}{4} \) containers. To convert \( 3 \frac{3}{4} \) into an improper fraction, we calculate: \[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \] Next, to find out how much sugar is in one container, we divide the total amount of sugar by the number of containers: \[ \text{Sugar per container} = \frac{10 \text{ tons}}{\frac{15}{4}} = 10 \times \frac{4}{15} = \frac{40}{15} \] Now we simplify \( \frac{40}{15} \) by finding the greatest common divisor of \( 40 \) and \( 15 \), which is \( 5 \): \[ \frac{40}{15} = \frac{40 \div 5}{15 \div 5} = \frac{8}{3} \] Now, we convert \( \frac{8}{3} \) into a mixed number. This can be done by dividing \( 8 \) by \( 3 \): \[ 8 \div 3 = 2 \text{ remainder } 2 \] So, as a mixed number, \( \frac{8}{3} \) is: \[ 2 \frac{2}{3} \] Therefore, one container can hold \( 2 \frac{2}{3} \) tons of sugar.