Question

samantha went to the grocery store and purchased cans of soup and frozen dinners. each can of soup has 350 mg of sodium and each frozen dinner has 700 mg of sodium. samantha purchased a total of 9 cans of soup and frozen dinners which collectively contain 3850 mg of sodium. determine the number of cans of soup purchased and the number of frozen dinners purchased.

Explanation:

Step1: Define Variables

Let \( x \) be the number of cans of soup and \( y \) be the number of frozen dinners. We have two equations:

1. \( x + y = 9 \) (total number of items)
2. \( 350x + 700y = 3850 \) (total sodium)

Step2: Simplify the Second Equation

Divide the second equation by 350: \( x + 2y = 11 \)

Step3: Subtract the First Equation

Subtract \( x + y = 9 \) from \( x + 2y = 11 \):
\( (x + 2y) - (x + y) = 11 - 9 \)
\( y = 2 \)

Step4: Find \( x \)

Substitute \( y = 2 \) into \( x + y = 9 \):
\( x + 2 = 9 \)
\( x = 7 \)

Answer:

Number of cans of soup: 7, Number of frozen dinners: 2