Question

David 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 550 mg of sodium. David purchased twice as many cans of soup as frozen dinners and they all collectively contain 2100 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

Answer 1

4 cans of soup and 2 frozen dinners.

Explanation:

Let us call
`s` the number of cans of soup David bought, and
`f` the number of frozen dinners.

We know that David bought twice as many cans of soup as frozen dinners; therefore,

`s=2f.`

We also know that each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium—and for all items David bought, collectively they contain 2100 mg of sodium; therefore, we have

`250s+550f=2100.`

Thus, we have two equations

(1).
`s=2f`

(2).
`250s+550f=2100`

and we solve them by substituting the value of
`s=2f` from equation(1) into equation(2):

`250(2f)+550f=2100\\\\\\500f+550f=2100\\\\1050f= 2100\\\\\\\boxed{f = 2 }`

David bought 2 frozen dinners.

And the number of cans of soup bought is

`s=2f`

`s=2*2\\\\\boxed{s=4}`

David bought 4 cans of soup.