One day, I did not have the exact number of dollar bills, so I gave her a twenty-dollar bill so that she would give me change for the cost of my haircut (which costs less than ten dollars). I would then have enough dollar bills to give her a tip, assuming that she gave me all one-dollar bills.
To my surprise, I discovered that my barber thought I was a senior citizen (people 62 or older get one dollar off the regular price of a haircut) because she gave me one dollar too much in change. I was tipping her 37.5% (based on a regular haircut), but how much did my barber think I had been tipping her (based on a senior citizen haircut)? What is the cost of a senior citizen haircut?
Extra Credit: How much do you think I will tip my barber next time?
Let x = the cost of a regular haircut.
Let x-1 = the cost of a senior citizen haircut.
Then x + .375x = whole number of dollars (cost of haircut plus tip)
So 1.375x = whole number of dollars
And 1 3/8 x = whole number of dollars
Therefore x must be a multiple of 8.
If x = 8, Then the total of the haircut and tip is 11 dollars.
If x = 16, Then the total is 22 dollars, but x must be less than 10 dollars.
So the cost of a haircut is $8.00, and
the cost of a senior citizen haircut is $7.00.
I normally tipped her $3.00 on an eight dollar haircut for 37.5%.
But she thought I was tipping her $4.00 on a seven dollar haircut for 57.1%!
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