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Dan bought [tex]\( x \)[/tex] pounds of potatoes for \[tex]$0.85 per pound and \( y \) pounds of grapes for \$[/tex]1.29 per pound. The total cost was less than \$5. Which inequality represents his purchase?
A. [tex]\( 1.29x + 0.85y \ \textless \ 5 \)[/tex]
B. [tex]\( 1.29x + 0.85y \ \textgreater \ 5 \)[/tex]
C. [tex]\( 0.85x + 1.29y \ \textgreater \ 5 \)[/tex]
To determine the correct inequality representing Dan's purchase, let's analyze his spending step-by-step:
1. Cost of Potatoes: Dan buys [tex]\( x \)[/tex] pounds of potatoes. Given the cost per pound is \[tex]$0.85, the total cost for the potatoes can be expressed as:
\[
\text{Cost of potatoes} = 0.85x
\]
2. Cost of Grapes: Dan buys \( y \) pounds of grapes. Given the cost per pound is \$[/tex]1.29, the total cost for the grapes can be expressed as: [tex]\[
\text{Cost of grapes} = 1.29y
\][/tex]
3. Total Cost: The overall cost for both the potatoes and grapes is the sum of the individual costs: [tex]\[
\text{Total cost} = 0.85x + 1.29y
\][/tex]
4. Cost Constraint: Dan's total expenditure was less than \$5, which can be written as: [tex]\[
0.85x + 1.29y < 5
\][/tex]
Therefore, the correct inequality that represents Dan's purchase is: [tex]\[
0.85x + 1.29y < 5
\][/tex]
So, the correct answer is: [tex]\[
\boxed{0.85x + 1.29y < 5}
\][/tex]
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