Question

Chris bought 2 chicken sandwiches and 3 bowls of vegetable soup for $16.50. Jim bought 1 chicken sandwich and 2 bowls of vegetable soup for $9.50. What was the cost of a bowl of soup? A) $4.50 B) $2.50 C) $5.50 D) $3.25​

Answer 1

Explanation:

This is a system of equations, best solved by using the elimination method. But first we have to come up with our 2 equations that represent the system. Let's call the chicken sandwiches "c" and the bowls of soup "b".

If Chris bought 2 chicken sandwiches and 3 bowls of soup for $16.50, his equation is:

2c + 3b = 16.50

If Jim bought 1 sandwich and 2 bowls of soup for $9.50, then his equation is:

1c + 2b = 9.50

We put these together, one above the other, lining up the variables:

2c + 3b = 16.50

1c + 2b = 9.50

If we multiply the second equation by -2 we can eliminate the c variable. Multiplying the second equation by -2 changes only that equation, making the "new" system:

2c + 3b = 16.50

-2c - 4b = -19.00

When we add straight down each column, the c's cancel each other out (they subtract away) and in the b column we have -1b, and in the answer column, we have -2.50.

That equation is -b = -2.50 or b = 2.50

A bowl of soup costs $2.50, choice B