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Question

An international cruise company offers its guests traveler credit cards when they are aboard. When a customer makes a purchase using his traveler card in a currency other than dollars, the bank converts the purchase price at the daily foreign exchange rate and then charges a 3.5% fee on the converted cost. Mr. Jabar is on a cruise off the coast of Peru. He used his traveler card for a purchase that cost 950 centimos (Peruvian currency). The bank posted a charge of $14.23 to his account that included the 3.5% fee.

Question: A bank in Peru sells a prepaid credit card worth 1800 centimos. Mr. Jabar can buy the prepaid card using dollars at the daily exchange rate with no fee, but he will lose any money left unspent on the prepaid card. What is the least amount of the 1800 centimos on the prepaid card Mr. Jabar must spend for the prepaid card to be cheaper than charging the same purchases on the traveler card? Round your answer to the nearest whole number of centimo.

Answer 1

The purchase made is X.

It is increased by 3.5%. So

100% + 3.5% = 103.5% = 1.035

1.035X = 14.23

X = 14.23 / 1.035 = 13.75

So 13.75 is 950 centimos...

Therefore $1 = 69.1 centimos is the current exachange rate

The pre-paid card is 1800 centimos = 1800/69.1 = $26.05

1.035 n = 26.05

n = 25.16 = 1738.5