Question

barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. she wrote an equation to find the number of bottles she needs to sell to earn $100.
1.25x + 1.49 = 100
what error did barbara make in writing the equation?
barbara’s equation did not consider the number of bottles of water.
barbara’s equation did not consider the number of bottles of iced tea.
barbara’s equation did not use the correct price for the bottles of iced tea.
barbara’s equation did not use the correct total for sales.

Explanation:

To determine the error, we analyze the equation structure. Let \( x \) be the number of water bottles and \( y \) be the number of iced tea bottles. The correct revenue equation should be \( 1.25x + 1.49y = 100 \), as revenue from water is \( 1.25 \times \) (number of water bottles) and from iced tea is \( 1.49 \times \) (number of iced tea bottles). Barbara's equation \( 1.25x + 1.49 = 100 \) has no variable (like \( y \)) for the number of iced tea bottles, so she didn't account for that quantity. The price of iced tea (\( 1.49 \)) is correct, and the total sales target (\( 100 \)) is also correct. The equation does consider the number of water bottles (\( x \)), so the error is not accounting for the number of iced tea bottles.

Answer:

Barbara’s equation did not consider the number of bottles of iced tea.