Question

Owen went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 650 mg of sodium. Owen purchased a total of 19 cans of soup and frozen dinners which collectively contain 11000 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

Answer 1

Answer: 2 with the remainder of 200

Explanation:

first you are going to times 19 cans by 500 mg of sodium and get 9,500

then you are going to subtract 11,000 by 9,500 and get 1,500

lastly you are going to take 1,500 and divide it by 650.

in the end you will get 2 with the remainder of 200.

Answer 2

Owen bought
`9` cans of soup and
`10` cans of frozen dinners.

Explanation:

We can solve this problem by writing the linear equation system that represents the situation.

Let be ''x'' the number of cans of soup purchased and ''y'' the number of frozen dinners purchased.

By reading the question we can write the following linear equation system :

`x+y=19` (I)

`x.(500)+y.(650)=11000` (II)

Working with the equation (I) we find that
`x=19-y` (III)

If we replace (III) in (II) :

`(19-y).(500)+y.(650)=11000`

`9500-500y+650y=11000`

`150y=1500`

`y=10`

We find that Owen bought
`10` cans of frozen dinners.

If we replace the value of ''y'' in (I) :

`x+10=19`

`x=9`

We find that Owen bought
`9` cans of soup.