Answer :
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]
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]
