Tyler went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 300 mg of sodium and each frozen dinner has 550 mg of sodium. Tyler purchased twice as many cans of soup as frozen dinners and they all collectively contain 5750 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

The number of cans of soup purchased is 10 and number of frozen dinner purchased is 5.

Given that,

Based on the above information, the calculation is as follows

s = 2d

And,  

300s + 550d = 5,750

Now put the value of s in the above equation  

300(2d) + 550d = 5,750

600d + 550d = 5,750

1,150d = 5,750

d = 5

So, s = 2(5)

= 10

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Tyler purchased 10 cans of soup and 5 frozen dinners.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of sodium per can of soup = 300 mg

Amount of sodium per frozen dinner = 550 mg

They all collectively contain 5,750 mg of sodium

Tyler purchased twice as many cans of soup as frozen dinners

2. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

Let s to represent the number of cans of soup Tyler purchased

Let d to represent the number of frozen dinners Tyler purchased

Let's write our equation of systems:

s = 2d (1st equation)

300s + 550d = 5,750 (2nd equation)

Substituting s and solving for d in the 2nd equation:

300s + 550d = 5,750

300 * 2d + 550d = 5,750

600d + 550d = 5,750

1,150d = 5,750

d = 5,750/1,150

d = 5 ⇒ s = 2 * 5 = 10

Tyler purchased 10 cans of soup and 5 frozen dinners.

Let's prove d = 5 and s = 10 are correct:

300 * 10 + 550 * 5 = 5,750

3,000 + 2,750 = 5,750

5,750 = 5,750

We proved d = 5 and s = 10 are correct