Question

The cost of a ham sandwich at a deli varies directly with the number of sandwiches. If the cost is $54 when there are 9 sandwiches, what is the cost of the sandwiches when there are 3?

Answer 1

To determine the cost of 3 sandwiches when the cost of 9 sandwiches is $54, divide the total cost by the number of sandwiches to find the unit price, which is $6. Then multiply the unit price by 3 to get the total cost for 3 sandwiches, which is $18.

Step-by-step explanation:

The student's question involves direct variation, which is a concept in mathematics where the cost of an item is directly proportional to the quantity.

Given that the cost of 9 sandwiches is $54, we can find the unit price per sandwich by dividing the total cost by the number of sandwiches. This gives us:

$$\text{Unit price} = \frac{\text{Total cost}}{\text{Number of sandwiches}} = \frac{\$54}{9} = \$6.$$

Once the unit price is established, we can multiply it by the desired number of sandwiches to find the total cost for any number of sandwiches. Therefore, to find the cost for 3 sandwiches, we would calculate:

$$\text{Cost for 3 sandwiches} = \text{Unit price} \times 3 = \$6 \times 3 = \$18.$$

So the cost of 3 sandwiches would be $18.