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# Math

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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
+36457
+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
+2540
+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
+36457
+1

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

-b = -2.50

b = \$ 2.50

ElectricPavlov  Apr 16, 2022
#4
+2540
+1

Happens to the best of us lol...

BuilderBoi  Apr 16, 2022