Question
Gabriel used the expression 2.5x + 2y – 2 to represent his total cost, and 28 – 2.5x – 2y to represent the amount of change he should receive from $30. What was Gabriel’s error?
Answers
GPT-4o mini
Gabriel's expressions for total cost and change seem to be designed to manage a budget of $30. Let's analyze the two expressions:
1. **Total Cost:**
- \( C = 2.5x + 2y - 2 \)
where \( x \) and \( y \) likely represent quantities of items or types of expenses at specific costs per unit.
2. **Change:**
- \( \text{Change} = 28 - 2.5x - 2y \)
Assuming Gabriel is purchasing items costing \( 2.5 \) per unit of \( x \) and \( 2 \) per unit of \( y \) from a total of \( 30 \):
- To find the change, we would subtract the total cost from \( 30 \):
\[
\text{Change} = 30 - \text{Total Cost}
\]
However, Gabriel used \( 28 \) in his expression for change:
\[
\text{Change} = 28 - 2.5x - 2y
\]
This indicates that he inaccurately set the baseline for his change to be \( 28 \) instead of \( 30 \). The correct expression should be:
\[
\text{Change} = 30 - (2.5x + 2y – 2)
\]
Instead, it appears that he is removing the total not from \( 30 \) but from \( 28 \), likely failing to account for the additional $2.
Thus, Gabriel's error is that he miscalculated the starting amount for determining his change. The change should be calculated from \( 30 \) rather than \( 28 \). The correct amount of change would therefore have been,
\[
\text{Change} = 30 - (2.5x + 2y)
\]
In summary, Gabriel's error was using the baseline for change as \( 28 \) instead of correctly using \( 30 \).
1. **Total Cost:**
- \( C = 2.5x + 2y - 2 \)
where \( x \) and \( y \) likely represent quantities of items or types of expenses at specific costs per unit.
2. **Change:**
- \( \text{Change} = 28 - 2.5x - 2y \)
Assuming Gabriel is purchasing items costing \( 2.5 \) per unit of \( x \) and \( 2 \) per unit of \( y \) from a total of \( 30 \):
- To find the change, we would subtract the total cost from \( 30 \):
\[
\text{Change} = 30 - \text{Total Cost}
\]
However, Gabriel used \( 28 \) in his expression for change:
\[
\text{Change} = 28 - 2.5x - 2y
\]
This indicates that he inaccurately set the baseline for his change to be \( 28 \) instead of \( 30 \). The correct expression should be:
\[
\text{Change} = 30 - (2.5x + 2y – 2)
\]
Instead, it appears that he is removing the total not from \( 30 \) but from \( 28 \), likely failing to account for the additional $2.
Thus, Gabriel's error is that he miscalculated the starting amount for determining his change. The change should be calculated from \( 30 \) rather than \( 28 \). The correct amount of change would therefore have been,
\[
\text{Change} = 30 - (2.5x + 2y)
\]
In summary, Gabriel's error was using the baseline for change as \( 28 \) instead of correctly using \( 30 \).