Dylan 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 500 mg of sodium.
dylan purchased 3 times as many cans of soup as frozen dinners and they all
collectively contain 2500 mg of sodium. determine the number of cans of soup
purchased and the number of frozen dinners purchased.

Dylan purchased 2 frozen dinners and 6 cans of soup at the grocery store.

Step-by-step explanation:

Milligrams of sodium per can of soup = 250

Milligrams of sodium per frozen dinner = 500

Number of frozen dinners Dylan purchased = x

Number of cans of soup Dylan purchased = 3x

For finding the number of frozen dinners and cans of soup, we use this equation:

250 (3x) + 500 (x) = 2,500 (Milligrams that collectively they contain)

750x + 500x = 2,500

1,250x = 2,500

x = 2 (Dividing by 1,250 at both sides of the equation)

3x = 6 (Number of cans of soup)

Dylan purchased 2 frozen dinners and 6 cans of soup at the grocery store, 2 frozen dinners and 6 cans of soup will contain 2,500 milligrams of sodium (1,000 + 1,500).

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.