Question

Adrian went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 350 mg of sodium and each frozen dinner has 700 mg of sodium. Adrian purchased a total of 9 cans of soup and frozen dinners which collectively contain 5250 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

Answer:

Adrian would have to purchase 9 cans and 3 frozen dinners.

step-by-step explanation:

Let us consider the sodium is denoted by a variable "s"

Let us consider the can is denoted by a variable "c"

Each can of soup containing the sodium = s = 350 mg  

Each frozen dinner containing the sodium = s = 700 mg  

The number of cans purchased by Adrian = c = 9 cans

The total amount of sodium = 5250 mg

Total amount of sodium purchased by Adrian

in 9 cans = 9 × 35  = 3150 mg

Subtracting 5250 mg by 3150 mg will give 2100 mg

So,   5250 mg - 3150 mg = 2100 mg

Dividing 2100 mg by 700 mg of sodium of frozen sodium will give the value 3.

So, Adrian would have to purchase 3 frozen dinner.

Hence, Adrian would have to purchase 9 cans and 3 frozen dinners to collectively contain 5250 mg of sodium.

Verification:  

The total amount of sodium = 5250 mg

Total amount of sodium purchased by Adrian in 9

cans = 9 × 350 = 3150 mg

Total amount of sodium purchased by Adrian in 3 frozen dinners = 3 × 700 = 2100 mg

Total sodium = sodium purchased in cans + sodium purchased in frozen dinners

5250 = 3150 + 2100

5250 = 5250

L.HS = R.HS

Keywords: system of equation, word problem, variables

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