samantha went to the grocery store and purchased cans of soup and frozen dinners. each can of soup has 350…

Answer:

Let the number of cans of soup be $x$ and the number of frozen - dinners be $y$. We have the following system of equations: $\begin{cases}x + y=9\350x + 700y=3850\end{cases}$ From the first equation $y = 9 - x$. Substitute $y = 9 - x$ into the second equation: $350x+700(9 - x)=3850$ $350x + 6300-700x=3850$ $- 350x=3850 - 6300$ $-350x=-2450$ $x = 7$ Substitute $x = 7$ into $y = 9 - x$, we get $y=9 - 7=2$ So, the number of cans of soup is 7 and the number of frozen - dinners is 2.

Explanation:

Step1: Set up the equations

Let $x$ be soup cans, $y$ be frozen - dinners. Total number gives $x + y=9$, sodium amount gives $350x + 700y=3850$.

Step2: Solve for $y$ in the first equation

$y = 9 - x$

Step3: Substitute $y$ into the second equation

$350x+700(9 - x)=3850$

Step4: Expand and simplify

$350x + 6300-700x=3850$

Step5: Combine like - terms

$-350x=3850 - 6300$

Step6: Calculate the right - hand side

$-350x=-2450$

Step7: Solve for $x$

$x = 7$

Step8: Find $y$

Substitute $x = 7$ into $y = 9 - x$, get $y = 2$