At a concession​ stand, Three hot dog(s) and four hamburger(s) cost $13.25, four hot dog(s) and three hamburger(s) cost $13.00. Find the cost of one hot dog and the cost of one hamburger.

Respuesta :

cost of hot dog is $1.64 and cost of hamburger is $2.14

Step-by-step explanation:

Let the cost of hot dog be [tex]hd[/tex]

Let the cost of hamburger be [tex]hm[/tex]

It is given that cost of three hot dogs and four hamburgers is $13.25

So, [tex]3\times hd+4\times hm=13.25[/tex]               .....[tex](i)[/tex]

It is given that cost of four hot dogs and three hamburgers is $13.00

So,[tex]4\times hd +3\times hm=13[/tex]                    .....[tex](ii)[/tex]

[tex]4\times (ii)-3\times (i)\text{ gives,}[/tex]

[tex]4\times(4\times hd+3\times hm)=4\times 13\\-3\times(3\times hd+4\times hm)=3\times 13.5\\\\7\times hd=11.5\\hd=1.64[/tex]

Substitute [tex]hd[/tex] in [tex](ii)[/tex] to get [tex]hm[/tex],

[tex]4\times 1.64 + 3\times hm=13\\3\times hm=6.43\\hm=2.14[/tex]

Hence cost of hot dog is $1.64 and cost of hamburger is $2.14

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