Answer:
$90
Step-by-step explanation:
We can represent plates as p and cups as c. We can write the two sentences that describe the cost of plates and cups as
[tex]12p+6c=156[/tex]
,[tex]12p+18c=228[/tex].
We're told to find the cost of 9 plates or 9p.
[tex]\dotfill[/tex]
There are many ways to get the value of p, we can use
(rearranging the variables in one equation and plugging that into the other one);
(subtracting the equations to get rid of an unnecessary variable).
For this case, we can use the elimination method, but we must have equivalent c terms.
We can multiply the first equation by 3 so both c terms are 18c.
[tex]3(12p+6c=156)=36p+18c=468[/tex]
Now, we can subtract each equation to eliminate the c values!
[tex]\:\:\:(36p+18c=468)\\\underline{-(12p+18c=228)}\\24p=240[/tex]
[tex]p=10[/tex]
So, 9p = 9(10) = 90!