alexa went to the grocery store and purchased cans of soup and frozen dinners - Mariah went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 250 mg of sodium and each frozen dinner has 450 mg of sodium. Mariah purchased twice as many frozen dinners as cans of soup and they all collectively contain 7200 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.

Sahil Khan (last edited 3 months ago)

Let x represents each can of soup and y represents each frozen dinner.

Mariah purchased thrice as many frozen dinners so, the equation to represent this will be

x = 3y or equation 1

Each can has 250 mg of sodium and frozen dinner has 450 mg of sodium, and they contain 7200 mg of sodium, so the equation to represent this will be

250 x + 450 y = 7200 or equation 2

Plug in x = 3y in equation 2, and solve for y.

250 (3y) + 450 y = 7200

750 y + 450 y = 7200

1200 y = 7200

y = 6.

This means that the number of frozen dinners purchased by Mariah are 6.

Plugging in y = 6, in the equation 1, we get x = 18.

This means that Mariah purchases 18 cans of soup.