Barbara made an error in writing her equation to find the number of bottles she needs to sell to earn \[tex]$100. Let's analyze the problem step-by-step:
1. Identify the cost per bottle:
- Iced tea: \$[/tex]1.49 per bottle
- Water: \[tex]$1.25 per bottle
2. Identify the target amount:
- Barbara wants to earn a total of \$[/tex]100.
3. Formulate the correct equation:
- Let [tex]\( x \)[/tex] represent the number of bottles of water sold.
- Let [tex]\( y \)[/tex] represent the number of bottles of iced tea sold.
- The total earnings from water sales would be [tex]\( 1.25 \times x \)[/tex].
- The total earnings from iced tea sales would be [tex]\( 1.49 \times y \)[/tex].
4. Combine these to form the total earnings equation:
- The correct equation should sum these earnings to equal \$100, hence: [tex]\( 1.25x + 1.49y = 100 \)[/tex].
However, Barbara's equation is:
[tex]\[ 1.25x + 1.49 = 100 \][/tex]
This equation is incorrect. Let's identify the specific error:
- Barbara included the variable [tex]\( x \)[/tex] (number of bottles of water) correctly.
- Barbara did not correctly include the variable [tex]\( y \)[/tex] (number of bottles of iced tea).
Thus, the error Barbara made was in not considering the number of bottles of iced tea in her equation.
Therefore, the correct answer is:
Barbara's equation did not consider the number of bottles of iced tea.
