Answer:
Cans of soup = 10
Frozen dinners = 5
Explanation:
To determine the number of cans of soup and frozen dinners Caleb purchased, set up and solve a system of equations based on the given information.
Let x be the number of cans of soup Caleb purchased.
Let y be the number of frozen dinners Caleb purchased.
Each can of soup has 200 mg of sodium and each frozen dinner has 500 mg of sodium. The total amount of sodium in the purchased cans and frozen dinners is 4500 mg. Therefore:
Caleb purchased a total of 15 cans of soup and frozen dinners. Therefore:
To solve the system of equations, rearrange the second equation to isolate x:
Substitute this into the first equation to eliminate the term in x, and solve for y:
Therefore, Caleb purchased 5 frozen dinners.
Substitute the found value of y into the rearranged second equation and solve for x:
Therefore, Caleb purchased 10 cans of soup.