Question

Madison went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 700 mg of sodium. Madison purchased 2 more frozen dinners than cans of soup and they all collectively contain 7400 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

Answer 1

Madison purchased 5 cans of soup and 7 frozen dinners.

Step-by-step explanation:

Given,

Quantity of sodium in each soup can = 500 mg

Quantity of sodium in each frozen dinner = 700 mg

Total quantity = 7400

Let,

Number of soup cans purchased = x

Number of frozen dinners purchased = y

According to given statement;

500x+700y=7400        Eqn 1

y = x+2        Eqn 2

Putting value of y from Eqn 2 in Eqn 1

$500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000$

Dividing both sides by 1200

$\frac{1200x}{1200}=\frac{6000}{1200}\\x=5$

Putting x=5 in Eqn 2

$y=5+2\\y=7$

Madison purchased 5 cans of soup and 7 frozen dinners.

Keywords: linear equation, substitution method

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