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At a concession​ stand,three hot dog(s) and two hamburger(s) cost ​$8.25​;two hot dog(s) and three hamburger(s) cost ​$8.00. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog​?

 Jul 31, 2020
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At a concession​ stand,three hot dog(s) and two hamburger(s) cost ​$8.25​;two hot dog(s) and three hamburger(s) cost ​$8.00. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog​?  

 

                                                              3 Dogs + 2 Burgers = 8.25    (1)  

                                                              2 Dogs + 3 Burgers = 8.00    (2)  

 

Multiply equation (1) by 2                       6D + 4B = 16.50                    (3)  

Multiply equation (2) by 3                       6D + 9B = 24.00                    (4)  

 

Subtract equation (3) from (4)                        5B  =  7.50  

Divide both sides by 5                                       B  =  1.50   One Burger costs $1.50  

 

Substitute 1.50 for B in (1)                      3D + (2)(1.50)  =  8.25  

                                                                3D + 3.00         =  8.25  

Subtract 3.00 from both sides                                    3D  =  5.25  

Divide both sides by 3                                                  D  =  1.75   One Dog costs $1.75  

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 Jul 31, 2020

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