Question

Bryan and Jadyn had barbeque potato chips and soda at a football party. Bryan ate 4 oz of chips and drank 1 cup of soda for a total of 600mg of sodium. Jadyn ate 1 oz of chips and drank 4 cups of soda for a total of 300mg of sodium. How much sodium is in 1 oz of chips and how much is in 1 cup of soda?

Answer 1

1 oz of chips has 140 mg of sodium, and 1 cup of soda has 40 mg of sodium.

Explanation:

This question is solved by a system of equations.

I am going to say that:

x is the amount of sodium in 1oz of chips.

y is the amount of sodium in 1 cup of soda.

Bryan ate 4 oz of chips and drank 1 cup of soda for a total of 600mg of sodium.

This means that
`4x + y = 600`, also
`y = 600 - 4x`

Jadyn ate 1 oz of chips and drank 4 cups of soda for a total of 300mg of sodium.

This means that:

`x + 4y = 300`

From the first equation, we have that
`y = 600 - 4x`. So

`x + 4(600 - 4x) = 300`

`x + 2400 - 16x = 300`

`15x = 2100`

`x = (2100)/(15)`

`x = 140`

`y = 600 - 4x = 600 - 4*140 = 40`

1 oz of chips has 140 mg of sodium, and 1 cup of soda has 40 mg of sodium.