Question

be an actuary.

1. a cruise ship made a trip to guam and back. the trip there took 12 hours and the trip back took nine hours. it averaged 20 mph on the return trip. find the average speed of the trip there.
2. aaron has saved up $600 to take a vacation for his upcoming spring break but is unsure how many nights he can afford to stay in a hotel. the hotel he wants to stay in charges $99.95 per night plus tax for a room. a tax of 8% is applied to the room rate, and an additional resort fee of $15.00 is charged nightly by the hotel. how many nights can aaron afford to stay in the hotel? (round down)
3. the gas mileage for peters car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. the cars gas tank has 17 gallons of gas at the beginning of a trip. if peters car travels at an average speed of 50 miles per hour, how much gas is remaining in the car after travelling 200 miles? (round to the nearest tenth of a gallon)
4. an international bank issues its traveler credit cards worldwide. when a customer makes a purchase using a traveler card in a currency different from the customers home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost.

sara lives in the united states but is on vacation in india. she used her traveler card for a purchase that cost 602 rupees (indian currency). the bank posted a charge of $9.88 to her account that included the 4% fee.
what foreign exchange rate, in indian rupees per one u.s. dollar, did the bank use for saras charge?

1. ming and carlos are selling cookie dough for a school fundraiser. customers can buy packages of chocolate chip cookie dough and packages of gingerbread cookie dough. carlos sold 8 packages of chocolate chip cookie dough and 12 packages of gingerbread cookie dough for a total of $364. ming sold 1 package of chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $93. find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.

Explanation:

Step1: Set up equations

Let \(x\) be the cost of one package of chocolate chip cookie dough and \(y\) be the cost of one package of gingerbread cookie dough.
We have the system of equations:
\(

$$\begin{cases}8x + 12y=364\\x + 4y=93\end{cases}$$

\)
From the second equation \(x=93 - 4y\)

Step2: Substitute

Substitute \(x = 93-4y\) into the first equation:
\(8(93 - 4y)+12y=364\)
\(744-32y + 12y=364\)
\(744-20y=364\)
\(-20y=364 - 744\)
\(-20y=-380\)
\(y = 19\)

Step3: Find \(x\)

Substitute \(y = 19\) into \(x=93 - 4y\)
\(x=93-4\times19\)
\(x=93 - 76\)
\(x = 17\)

Answer:

The cost of one package of chocolate chip cookie dough is \(\$17\) and the cost of one package of gingerbread cookie dough is \(\$19\)