Question

The expression 1.5 + 1.75x represents Gerald's total cost, in dollars, for buying some magnets and a keychain at a souvenir shop. Which statement is correct?

1) The magnets cost $1.50 each and the keychains cost $1.75 each.
2) The magnets cost $1.75 each and the keychains cost $1.50 each.
3) The magnets cost $1.50 each and the keychains cost $1.50 each.
4) The magnets cost $1.75 each and the keychains cost $1.75 each.

Answer 1

The correct statement is that the magnets cost $1.75 each and the keychain costs $1.50. This is deduced from the expression 1.5 + 1.75x, where 1.5 represents the fixed cost of the keychain and 1.75x represents the variable cost of x number of magnets.

Step-by-step explanation:

The expression 1.5 + 1.75x represents Gerald's total cost, in dollars, for buying some magnets and a keychain at a souvenir shop. The 1.5 represents a fixed cost, which is likely the price of a single item, such as the keychain. The term 1.75x represents a variable cost, which depends on the number of items purchased; in this case, 'x' is the number of magnets, and 1.75 is the cost per magnet. Therefore, each magnet costs $1.75 and the keychain costs $1.50 each. This corresponds to statement 2, which asserts that the magnets cost $1.75 each, and the keychain costs $1.50. We can confirm this since the fixed cost cannot depend on 'x', thus it aligns with the cost of a single keychain, while the variable cost must be associated with the number of items (magnets) bought multiplied by the cost per item.