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Bill bought 2 chicken sandwiches and 3 bowls of vegetable soup for $16.50. Sam bought 1 chicken sandwich and 2 bowls of vegetable soup for $9.50. What was the cost of a bowl of a soup?

 Apr 16, 2022
 #1
avatar+36417 
+1

Given:

  2c + 3b = 16.50

  1c + 2b = 9.50       <===== multiply this equation by -2     then add to top equation ( this will eliminate 'c')

  -2c -4b = -19.00     now add the top and the bottom

         -b = -2.50

            b = $ 5.00

 Apr 16, 2022
edited by ElectricPavlov  Apr 16, 2022
edited by ElectricPavlov  Apr 16, 2022
 #2
avatar+1384 
+1

\(c = \) Number of chicken sandwiches purchased

\(s\) = Number of vegetable soups purchased

 

\(2c+3s=16.50\)          (1)

\(c+2s=9.50\)              (2)

 

Subtract \(2s\) from both sides: \(c=9.50-2s\)

 

Substitute into (1): \(2(9.50-2s)+3s=16.50\)

 

Simplify: \(19-4s+3s=16.50\)

 

Solve: \(s = \color{brown}\boxed{2.50}\)

 Apr 16, 2022
 #3
avatar+36417 
+1

Ha!   BB is correct !    I do not know why I typed that last line frown     Corrected... THANX, BB !

   -b = -2.50

            b = $ 2.50

ElectricPavlov  Apr 16, 2022
 #4
avatar+1384 
+1

Happens to the best of us lol...

BuilderBoi  Apr 16, 2022

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