Question

Lincoln went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. Lincoln purchased a total of 13 cans of soup and frozen dinners which collectively contain 4450 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

Answer 1

Answer: 9 cans of soup and the 4 frozen dinners were purchased

Step-by-step explanation:

Let x represent the number of cans of soup purchased.

Let y represent the number of frozen dinners purchased.

Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that

x + y = 13

Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. The 13 cans of soup and frozen dinners which he purchased collectively contain 4450 mg of sodium. This means that

250x + 550y = 4450 - - - - - - - - -1

Substituting x = 13 - y into equation 1, it becomes

250(13 - y) + 550y = 4450

3250 - 250y + 550y = 4450

- 250y + 550y = 4450 - 3250

300y = 1200

y = 1200/300

y = 4

Substituting y = 4 into x = 13 - y, it becomes

x = 13 - 4 = 9

Answer 2

We can solve with a system of equations, and use c for the amount of cans of soup and f for the amount of frozen dinners.


The first equation will represent the amount of sodium. We know the (sodium in one can times the number of cans) plus (sodium in one frozen dinner times the number of dinners) is the expression for the total sodium. We also know the total sodium is 4450, so:


250c + 550f = 4450


The second equation is to find how many of each item are purchased:


c + f = 13


Solve for c in the second equation:


c = 13 - f


Plug this in for c in the first equation:


250(13-f) + 550f = 4450


3250 - 250f + 550f = 4450


300f = 1200


f = 4


Now plug the value for f into the second equation:


c + 4 = 13


c = 9


The answer is 9 cans of soups and 4 frozen dinners.