At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents [tex]\(x\)[/tex], the number of microwave burritos, and [tex]\(y\)[/tex], the number of peanut butter sandwiches, she can eat each week?

A. [tex]\(490x + 700y \ \textless \ 4000\)[/tex]
B. [tex]\(490x + 700y \leq 4000\)[/tex]
C. [tex]\(490x + 700y \ \textgreater \ 4000\)[/tex]
D. [tex]\(490x + 700y \geq 4000\)[/tex]



Answer :

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]