Question

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.

Answer 1

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 $hd$

Let the cost of hamburger be $hm$

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

So, $3\times hd+4\times hm=13.25$               .....$(i)$

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

So,$4\times hd +3\times hm=13$                    .....$(ii)$

$4\times (ii)-3\times (i)\text{ gives,}$

$4\times(4\times hd+3\times hm)=4\times 13\\-3\times(3\times hd+4\times hm)=3\times 13.5\\\\7\times hd=11.5\\hd=1.64$

Substitute $hd$ in $(ii)$ to get $hm$,

$4\times 1.64 + 3\times hm=13\\3\times hm=6.43\\hm=2.14$

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