Question

A gasoline station in Manila, Philippines, charges 38.46 pesos per liter of unleaded gasoline at a time when one U.S. dollar (USD) buys 47.15 pesos (PHP). The car you are driving has a gas tank with a capacity of 14 U.S. gallons and gets 24 miles per gallon. (a) What is the cost of unleaded gasoline in Manila in USD per gallon? (b) How much would a tankful of unleaded gasoline for your car cost in USD? (c) Suppose that you have only PHP 1255 (a day's wage for an elementary school teacher) and the car's tank is almost empty. How many miles can you expect to drive if you spend all your money on gasoline?

Short answer

Answer: The cost of unleaded gasoline in Manila is 3.08 USD per gallon, a tankful for the car would cost 43.12 USD, and after spending PHP 1255 on gasoline, one can expect to drive approximately 207.36 miles.

Step-by-step solution

(Step 1: Convert the gasoline price from pesos per liter to USD per liter)

First, we need to convert the price of gasoline from pesos per liter to USD per liter. To do this, we will divide the given price in pesos per liter (38.46 PHP/L) by the given exchange rate (47.15 PHP per 1 USD): Cost in USD per liter = 38.46 PHP/L / 47.15 PHP/USD = 0.815 USD/L.

(Step 2: Convert the gasoline price in USD per liter to USD per gallon)

Next, we need to convert the price from USD per liter to USD per gallon. There are approximately 3.78541 liters in 1 gallon; hence, Cost in USD per gallon = 0.815 USD/L * 3.78541 L/gal = 3.08 USD/gal. This is the answer to part (a).

(Step 3: Calculate the total cost of a tankful of unleaded gasoline in USD)

To find the total cost of a tankful of gasoline, we will multiply the price per gallon found in step 2 by the car's tank capacity (14 gallons): Total cost of a tankful = 14 gal * 3.08 USD/gal = 43.12 USD. This is the answer to part (b).

(Step 4: Calculate the number of gallons that can be bought with PHP 1255)

Now we need to find out how many gallons of gasoline can be bought with PHP 1255. First, convert the amount from PHP to USD: Amount in USD = 1255 PHP * 1 USD / 47.15 PHP = 26.62 USD. Next, divide the amount in USD by the cost of gas in USD per gallon to find the number of gallons that can be bought: Number of gallons = 26.62 USD / 3.08 USD/gal = 8.64 gal.

(Step 5: Calculate the miles that can be driven with the purchased gasoline)

Finally, we will multiply the number of gallons purchased by the car's fuel efficiency (24 miles per gallon) to find the number of miles that can be driven after spending PHP 1255: Miles driven = 8.64 gal * 24 miles/gal = 207.36 miles. This is the answer to part (c). To summarize: a) The cost of unleaded gasoline in Manila is 3.08 USD per gallon. b) A tankful of unleaded gasoline for your car would cost 43.12 USD. c) If you spend all your money (PHP 1255) on gasoline, you can expect to drive approximately 207.36 miles.