On his daily commute Bill always crosses a certain toll bridge

Let x be the number of days Bill commutes on the certain toll bridge. Since he
crosses the toll bridge twice daily, in order for the discount pass to become a
financial benefit for Bill

\(2x(1.5 - 0.8*1.5) > 50\) -> \(0.6x > 50\) -> \(x > \frac{50}{0.6}\) or \(83.33\)

Therefore, it will take 84(Option D) days for the discount pass to become a financial benefit for Bill.

Solution

Given:

• Bill crosses a certain toll bridge exactly twice a day
• Discount pass for $50 can decrease the cost of the toll by 20%
• Toll costs $1.50 per crossing

To find:

• After how many days of commuting will buying the discount pass result in a financial benefit for Bill

Approach and Working:
Let’s assume that it will take d days for Bill to get financial benefit from buying the pass

• The cost reduction in a day due to the pass = 20% of (1.5 * 2) = 0.6

As the investment in buying the pass is $50, to get financial benefit Bill must recover the investment totally

• We already know $0.6 is recovered in a day

Hence, if Bill gets financial benefits in d days, then we can write

• 0.6 * d > 50
Or, d > 83.3

As d denotes an integer, the minimum value of d will be 84

Hence, the correct answer is option D.

Answer: D

We can let d = the number of days to get a financial benefit (i.e. profit)and create the equation:

50 + 0.8(3) x d = 3d

50 + 2.4d = 3d

50 = 0.6d

d = 50/0.6 = 500/6 = 83.33

Since d must be a whole number, we see that 83 days still yields a slight loss for Bill. We must round up to 84 in order for the discount pass to result in a financial benefit for Bill.

Alternate Solution:

Each day, Bill normally pays $3.00. If he receives a 20% discount by buying the discount pass, he will pay 0.8 x $3.00 = $2.40 each day, thus saving $0.60 per day. Since the pass costs $50.00, we see that he will take 50/0.6 = 83.33 days to break even. If we round this value down to 83 days, he has not quite broken even. Therefore, in order to get a financial benefit, we round 83.33 up to 84 days.


Answer: D

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