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pochemuha
3 years ago
5

A taxi service has two rates, as follows: Rate A charges a flat $2.50 for every mile; rate B charges $15 plus $1.50 per mile. At

least how many miles (expressed as a whole number) must one travel to make Rate B cheaper?
Mathematics
1 answer:
Marina CMI [18]3 years ago
4 0
One must travel 16 miles before rate B becomes the cheapest rate.
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11.42 boxes

Step-by-step explanation:

For the first box bought, there is a 100% chance of getting a unique toy (since you still don't have any). E₁ = 1.

After that, there is a 4 in 5 chance of getting a unique toy from the next box, the expected number of boxes required is:

E_2 = (\frac{4}{5})^{-1} = 1.25

For the next unique toy, there is now a 3 in 5 chance of getting it:

E_3 = (\frac{3}{5})^{-1} = 1.67

Following that logic, there is a 2 in 5 chance of getting the 4th unique toy:

E_4 = (\frac{2}{5})^{-1} = 2.5

Finally, there is a 1 in 5 chance to get the last unique toy:

E_5 = (\frac{1}{5})^{-1} = 5

The expected number of boxes to obtain a full set is:

E=E_1+E_2+E_3+E_4+E_5\\E=1+1.25+1.67+2.5+5\\E=11.42\ boxes

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