Samuel 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 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 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.

Question

Samuel 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 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 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.

Answer 1

Let's assume that Samuel purchased x cans of soup and y frozen dinners.

The amount of sodium from the cans of soup is 300x mg and the amount of sodium from the frozen dinners is 450y mg.

According to the information given, Samuel purchased 5 more frozen dinners than cans of soup. So, the equation representing the relationship between the number of frozen dinners (y) and the number of cans of soup (x) is:

y = x + 5

The total amount of sodium from the cans of soup and frozen dinners combined is 6000 mg. Therefore, we can write the equation as:

300x + 450y = 6000

So, the system of equations to determine the number of cans of soup purchased (x) and the number of frozen dinners purchased (y) is:

y = x + 5
300x + 450y = 6000

In this system, the variables are x (number of cans of soup purchased) and y (number of frozen dinners purchased).