Let's review the facts:
The tip was $0.90, which was 10% of the after tax cost.
The tax was 8% of the bill.
Let's make some algebra here and substitute in some variables!
The bill after tax and tip (or total bill) will be 'a'
The bill after tax will be 'b'
We know that the tip ($0.90) was 10% of the after tax cost (b):
$0.90 = 10% * b
We know that the total after tax and tip (a) equals the after tax cost (b) plus the tip:
a = b + $0.90
As you can see, we don't need to know that the tax was 8% of the bill in order to get these equations. That's our answer for the first question.
Now we can evaluate our second equation to figure out what the total bill (a) is.
a = b + $0.90
Let's get rid of that b so we only have the variable we're getting the value of.
In order to do so, we can use the first equation and find the value of b there:
0.90 = 0.10 * b
Divide both sides by .10:
0.90 / 0.10 = b
Evaluate:
9 = b
Now we can substitute 9 in for b in our other equation:
a = b + 0.9
a = 9 + 0.9
a = 9.9
So the total bill was 9.9; the answer to our second question.
