To address the problem, we need to determine the inequality that represents the constraint on Kira's sodium intake from eating microwave burritos and peanut butter sandwiches.
Given:
- Each burrito contains 490 milligrams of sodium.
- Each peanut butter sandwich contains 700 milligrams of sodium.
- Kira's weekly sodium intake should not exceed 4,000 milligrams.
We need to represent [tex]\( x \)[/tex] as the number of microwave burritos Kira eats in a week and [tex]\( y \)[/tex] as the number of peanut butter sandwiches she eats in a week.
To find the total sodium intake for the week from both types of food, we'll add the sodium from [tex]\( x \)[/tex] burritos and [tex]\( y \)[/tex] sandwiches:
[tex]\[ 490x \][/tex] milligrams of sodium from [tex]\( x \)[/tex] microwave burritos,
[tex]\[ 700y \][/tex] milligrams of sodium from [tex]\( y \)[/tex] peanut butter sandwiches.
Thus, the total sodium intake is given by:
[tex]\[ 490x + 700y \][/tex]
Kira's total sodium intake for the week should be no more than 4,000 milligrams, leading to the following inequality:
[tex]\[ 490x + 700y \leq 4000 \][/tex]
This inequality represents the condition that her sodium intake from burritos and sandwiches should not exceed the doctor's recommended weekly limit.
Thus, the correct inequality is:
[tex]\[ 490x + 700y \leq 4000 \][/tex]
