Answer:
Cost of one hot dog: $1.39 (rounded to the nearest hundredth)
Cost of one hambuger: $1.51 (rounded to the nearest hundredth)
Step-by-step explanation:
Let x and y be the cost of one hot dog and the cost of one hamburger, respectively. With the information given, a system of equations is obtained:
[tex]7x + 4y=15.75\\4x+7y=17.25[/tex]
There are a lot of methods to solve a system like this, let's try the substitution method:
The first step is solving one of the equation for one of the variables, let's solve x for the first equation:
[tex]x=\frac{15.75-4y}{7}[/tex]
Then, this value is substituted in the second equation and solved for the other variable:
[tex]4(\frac{17.75-4y}{7})+7y=17.25\\\frac{71}{7}-\frac{16y}{7}+7y=17.25\\- \frac{16y}{7}+ 7y=17.25-\frac{71}{7} \\\frac{33}{7}y=\frac{199}{28}\\ y=\frac{199(7)}{28(33)}\\ y=199/132=1.51\\[/tex]
Finally, the value of y is substituted in any of the equations and solved for x:
[tex]7x+4(1.5)=15.75\\x=\frac{15.75-6}{7} \\x=1.39[/tex]
