Math Snap

STEP 1

Assumptions1. Each can of soup contains350mg of sodium. Each frozen dinner contains700mg of sodium3. Samantha purchased a total of9 items (soup cans and frozen dinners)
4. The total sodium content of all items purchased is3850mg

STEP 2

Let's denote the number of soup cans as $s$ and the number of frozen dinners as $d$.

STEP 3

We can write two equations based on the problem. The first equation is based on the total number of items$$s + d =9$$

STEP 4

The second equation is based on the total sodium content$$350s +700d =3850$$

STEP 5

We can simplify the second equation by dividing all terms by350$$s +2d =11$$

STEP 6

Now we have a system of two equations\begin{align} s + d &=9 \\ s +2d &=11\end{align}

STEP 7

We can solve this system of equations by subtracting the first equation from the second$$(s +2d) - (s + d) =11 -9$$

STEP 8

This simplifies to$$d =2$$

STEP 9

Now that we have $d$, we can substitute it into the first equation to find $s$$$s +2 =9$$

olving for $s$ gives$$s =9 -2 =7$$So, Samantha purchased7 cans of soup and2 frozen dinners.