Okay, so you're basically given everything except the price of the taco. This problem, therefore, needs to be solved backward. (I felt that some info was missing, so I did some estimation).
So we're given that the grand total is #$13.80#. Also, we're told that the tip money was #$3.00#. First, let's subtract the tip from our total:
#color(green)$color(green)13.80# #color(red)-color(red)$color(red)3.00# #=# #10.80#
Okay, so without the tip, we have #$10.80#. Next, we have to take a look at the sales tax, which is #8%#. So this is the point that I estimated in order to get the right answer.
I subtracted #$2.50# (salad price) from #$10.80# and came out with #$8.30#. I then divided that by two since there are two tacos. I got #$4.15#. I knew that the price of each taco would be less than that since I started with the sales tax included, so I tried if #$4.00# was the price of each taco:
#$4.00 * 2 = $8.00# (price of taco x number of tacos)
#$8.00 + $2.50 = $10.50# (total price of tacos + price of salad)
#$10.50 * .08 = $0.84# (total price of meal x sales tax percentage)
#$0.84 * $10.50 = $11.34# (sales tax + total price of meal)
Definitely, #$11.34# is more than #$10.80#, so we need to pick a number smaller than #$4.00#. #$3.75# is my next estimate.
#$3.75 * 2 = $7.50# (price of taco x number of tacos)
#$7.50 + $2.50 = $10.00# (total price of tacos + price of salad)
#$10.00 * .08 = $0.80# (total price of meal x sales tax percentage)
#$0.80 * $10.00 = $10.80# (sales tax + total price of meal)
Okay, it worked! According to these calculations, each taco was #$3.75#.
Now, it's time to check if we did it right. Here is a formula that I created when I looked at the problem:
#([2 * x + $2.50] 1.08) + $3 = $13.80#
x= price of one taco
The price for two tacos is added to the price for salad, then multiplied by the sales tax. This value is added to the tip, which should yield #$13.80#.
#([2 * $3.75 + $2.50] 1.08) + $3 = $13.80#
#([$7.50 + $2.50] 1.08) + $3 = $13.80#
#([$10.00] 1.08) + $3 = $13.80#
#($10.80) + $3 = $13.80#
#$13.80 = $13.80# Looks good!
Hope this helps!
