Respuesta :
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:
[tex]\begin{gathered} 5x+7y=9432 \\ 4x+9y=10592 \end{gathered}[/tex]Multiply the first equation by 9 and the second equation by 7 to get,
[tex]\begin{gathered} 45x+63y=84888\ldots(a) \\ 28x+63y=74144\ldots(b) \end{gathered}[/tex]Subtract (b) from (a):
[tex]\begin{gathered} 45x-28x+63y-63y=84888-74144 \\ 17x=10744 \\ x=\frac{10744}{17} \\ x=632 \end{gathered}[/tex]We have x = 632. Put x = 632 in first equation:
[tex]\begin{gathered} 5(632)+7y=9432 \\ 3160+7y=9432 \\ 7y=6272 \\ y=896 \end{gathered}[/tex]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.
