SOLUTION: A couple does not wish to spend more than $50 for dinner at a restaurant. If a sales tax of 7% is added to the bill and they plan to tip 20% after the tax has been added, what is t

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Question 764479: A couple does not wish to spend more than $50 for dinner at a restaurant. If a sales tax of 7% is added to the bill and they plan to tip 20% after the tax has been added, what is the most they can spend for the meal? (Round your answer to the nearest cent.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the bill for the meal
before the sales tax is added
-----------------------------
+x+%2B+.07x+=+1.07x+ = amount of bill
after the sales tax is added
-------------------------------
+1.07x+%2B+.2%2A%28+1.07x+%29+ = amount
they paid after including the tip
----------------------------
Since $50 is the most they can spend,
+50+=+1.07x+%2B+.2%2A%28+1.07x+%29+
+50+=+1.07x%2A%28+1+%2B+.2+%29+
+50+=+1.07%2A1.2x+
+50+=+1.284x+
+x+=+38.94+
$38.94 is the most expensive meal they can order
check:
+1.07%2A38.94+=+41.67+
+41.67%2A1.2+=+50.004+
OK