Answer:
$8.5
Step-by-step explanation:
We need to propose a system of equations with the information provided to us.
two large pizzas and one small pizza cost $36:
[tex]2L+S=36[/tex]
where
[tex]L[/tex]: Large pizza
[tex]S:[/tex] Small pizza
and the difference in cost between a large and small pizza is $5.25:
[tex]L-S=5.25[/tex]
our system of equations is:
[tex]2L+S=36[/tex]
[tex]L-S=5.25[/tex]
We are asked for the price of small pizza, so we must manipulate the equations in such a way that adding or subtracting them removes the variable L and we are left with an equation for S.
Multiply the second equation of the system by -2
[tex](-2)(L-S=5.25)\\\\-2L+2S=-10.5[/tex]
and now we sum this with the first equation of the system:
[tex]-2L+2S=-10.5\\+(2L+S=36)\\-------------\\-2L+2L+2S+S=-10.5+36[/tex]
simplifying the result:
[tex]3S=25.5[/tex]
and solving for S (the price of a small pizza)
[tex]S=25.5/3\\S=8.5[/tex]
