A shipment of 14 tons of sugar is separated into containers of equal size. If the shipment fills $5 \frac{5}{6}$ containers, how much sugar can one container hold? Write your answer as a mixed number in simplest form.
Answer (1)
Set up the equation 5 6 5 x = 14 , where x is the amount of sugar one container can hold.
Convert the mixed number to an improper fraction: 5 6 5 = 6 35 , so the equation becomes 6 35 x = 14 .
Solve for x : x = 14 × 35 6 = 5 12 .
Convert the improper fraction to a mixed number: x = 2 5 2 . The amount of sugar one container can hold is 2 5 2 tons.
Explanation
Understanding the problem We are given that a shipment of 14 tons of sugar fills 5 6 5 containers. We need to find out how much sugar one container can hold.
Setting up the equation Let x be the amount of sugar (in tons) that one container can hold. Then, the total amount of sugar in 5 6 5 containers is 5 6 5 x . We are given that this amount is equal to 14 tons. So, we can write the equation:
5 6 5 x = 14
Converting to improper fraction First, we convert the mixed number 5 6 5 to an improper fraction:
5 6 5 = 6 5 × 6 + 5 = 6 30 + 5 = 6 35
So, our equation becomes:
6 35 x = 14
Solving for x Now, we solve for x by multiplying both sides of the equation by the reciprocal of 6 35 , which is 35 6 :
x = 14 × 35 6
We can simplify this expression:
x = 35 14 × 6 = 5 2 × 6 = 5 12
Converting to mixed number Finally, we convert the improper fraction 5 12 to a mixed number:
5 12 = 2 5 2
So, one container can hold 2 5 2 tons of sugar.
Final Answer Therefore, one container can hold 2 5 2 tons of sugar.
Examples
Understanding how to divide quantities into equal parts is useful in many real-life situations. For example, if you are distributing food supplies among a group of people, you need to calculate how much each person receives. Similarly, if you are dividing a total cost among several individuals, you need to determine each person's share. This problem demonstrates how to divide a quantity (14 tons of sugar) into equal parts based on the number of containers, which is a practical application of fractions and mixed numbers.
