Final answer:
Magan purchased 8 cans of soup and 3 frozen dinners.
Step-by-step explanation:
Let's assume that the number of cans of soup purchased is x and the number of frozen dinners purchased is y.
Given that each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium, we can set up the following system of equations based on the information provided:
x + y = 11 (equation 1)
350x + 650y = 4750 (equation 2)
To solve this system of equations, we can use the substitution method:
From equation 1, we can rearrange it to express x in terms of y:
x = 11 - y.
Substituting this expression for x in equation 2, we get: 3
50(11 - y) + 650y = 4750.
Simplifying the equation, we have:
3850 - 350y + 650y
= 4750.
Combining like terms, we get: 300y = 900.
Dividing both sides of the equation by 300, we find that y = 3.
Substituting this value of y back into equation 1, we can solve for x:
x + 3 = 11, so x = 8.
Therefore, Magan purchased 8 cans of soup and 3 frozen dinners.