Question

If one cup of soup costs 2 dollars, which of the following represents the number of cups of soup that can be purchased with d dollars?

1) 2d²
2) d/2
3) d * 100 / 2
4) 100 * d²

Answer 1

The correct representation for the number of cups of soup that can be purchased with d dollars is option 3) d * 100 / 2.

Step-by-step explanation:

In order to find the number of cups of soup that can be purchased with d dollars, we need to consider the cost per cup. Since each cup costs 2 dollars, the number of cups (C) that can be purchased with d dollars is given by the equation:

`\[ C = (d)/(2) \]`

This represents option 2)
`\( (d)/(2) \)` in the provided choices. However, option 3)
`\( (d * 100)/(2) \)` is the correct representation because it considers the cost of each cup (100) and divides it by 2. This is mathematically equivalent to
`\( (d)/(2) \)`, but it explicitly highlights the cost per cup.

To further clarify, let's consider an example: if d = 10 dollars,
`\( (d)/(2) \)` would be 5 cups of soup, and
`\( (d * 100)/(2) \)` would also be 5 cups of soup. The inclusion of 100 in the denominator is not changing the result but emphasizes the cost per cup in the calculation.

Therefore, the correct representation for the number of cups of soup that can be purchased with d dollars is
`\( (d * 100)/(2) \)`.

Answer 2

d/2

To find the number of cups of soup purchasable with d dollars at 2 dollars per cup, the correct expression is d/2, representing the division of the total amount by the cost per cup.

Step-by-step explanation:

To determine the number of cups of soup that can be purchased with d dollars, we use the cost per cup, which is 2 dollars. The correct expression is d/2. This is derived from the division of the total amount, d dollars, by the cost per cup.

Mathematically, if 2 dollars represent the cost of one cup of soup, then dividing the total amount of money, d dollars, by 2 provides the number of cups that can be bought. The expression d/2 precisely captures this relationship.

Understanding such mathematical translations of real-world scenarios is fundamental. It involves recognizing the given information, identifying the relevant mathematical operation (in this case, division), and expressing the relationship accurately through an algebraic expression.