Joshua went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 200 mg
of sodium and each frozen dinner has 400 mg of sodium.
Joshua purchased a total of 10 cans of soup and frozen
dinners which collectively contain 2400 mg of sodium.
Write a system of equations that could be used to
determine the number of cans of soup purchased and
the number of frozen dinners purchased. Define the
variables that you use to write the system.

c + f = 10

200c + 400f = 2400

Step-by-step explanation:

Let's say c is the number of cans of soup and f is the number of frozen dinners.

The total number of items is 10:

c + f = 10

The total amount of sodium is 2400 mg.  Each can of soup has 200 mg, and each frozen dinner has 400 mg.

200c + 400f = 2400

The problem doesn't ask you to solve the system, but I'll solve it anyway.  We can use substitution or elimination.  But first, simplify the second equation by dividing both sides by 200.

c + 2f = 12

Using elimination, subtract the first equation.

f = 2

Plug into either equation to find c:

c = 8

There are 8 cans of soup and 2 frozen dinners.

a² + b²= c²

24² + 7² = c²

c= 25