Question

The total amount of sodium in 5 hot dogs and 7 cups of cottage cheese is 9432 mg. The total amount of sodium in 4 hot dogs and 9 cups of cottage cheese is 10592 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

Answer 1

Given:

The total amount of sodium in 5 hot dogs and 7 cups of cottage cheese is 9432 mg. The total amount of sodium in 4 hot dogs and 9 cups of cottage cheese is 10592 mg.

To find:

The quantity of sodium in a hot dog and the quantity of sodium in a cup of the cottage.

Solution:

Let the quantity of sodium in a hot dog be x mg and the quantity of sodium in a cup of the cottage is y.

From the given information, we have:

`\begin{gathered} 5x+7y=9432 \\ 4x+9y=10592 \end{gathered}`

Multiply the first equation by 9 and the second equation by 7 to get,

`\begin{gathered} 45x+63y=84888\ldots(a) \\ 28x+63y=74144\ldots(b) \end{gathered}`

Subtract (b) from (a):

`\begin{gathered} 45x-28x+63y-63y=84888-74144 \\ 17x=10744 \\ x=(10744)/(17) \\ x=632 \end{gathered}`

We have x = 632. Put x = 632 in first equation:

`\begin{gathered} 5(632)+7y=9432 \\ 3160+7y=9432 \\ 7y=6272 \\ y=896 \end{gathered}`

Thus, the quantity of sodium in hot dogs is 632 mg and the quantity of sodium in a cup of cottage cheese is 896 mg.