Question: Alec is running for Class President. He thinks that if he can get three-quarters of the class to vote for him then there is no chance anyone else can beat him. Half of the class have already said they will vote for him but out of the remaining students, only 5 have said they are thinking about voting for him. He surveys the students who are thinking about voting for someone else, and changes his flyers to reflect the issues these students are concerned about. This results in a fifth of these students saying they'll vote for him. If Alec's class has 60 students and everyone who said they will vote for him does so, how many more votes does Alec need to reach his goal number of votes?
Answer: To calculate Alec's goal number of votes, we need to know that 60 students / 4 = 15 students is equal to one - quarter of the class students. Alec's goal is therefore 15 students * 3 quarters = 45 votes. Half of the class said they will vote for him, so there are already 60 students / 2 = 30 votes. Another 5 students are thinking about voting for him which leaves a total so far of 30 + 5 = 35 votes. This means there are 60 students - 35 voting for Alec = 25 students not voting for Alec. A fifth of these decided to vote, so this is a further 25 students / 5 = 5 votes. Alec is therefore receiving a total of 35 + 5 = 40 votes. So he has missed his goal by 45 goal votes - 40 actual votes = 5 votes. The answer is 5.

Question: Frankie and Carla played 30 games of ping pong against each other. Frankie won half as many games as did Carla. How many games did Carla win?
Answer: Let x be the number of games that Frankie won. Then the number of games Carla won would be 2 * x. And the sum of all the games would be x + 2 * x = 30 games. Thus, the expression simplifies to 3 * x = 30. And the value of x = 10 games. Therefore, the number of Carla's wins would be 2x = 20 games. The answer is 20.

Question: Roberto is out for a hike. He travels uphill at 2 MPH and downhill at 3MPH. The trail is 5 miles long. 60% is uphill and the rest is downhill. How long does it take him to complete it in minutes?
Answer: There is 3 miles uphill because 5 x .6 = 3. This takes him 1.5 hours because 3 / 2 = 1.5. This takes him 90 minutes because 1.5 x 60 = 90. 40% of the trail is downhill because 100 - 60 = 40. There are 2 miles of downhill because 5 x .4 = 2. This takes him 2 / 3 of an hour because 2 / 3 = (2 / 3). This takes him 40 minutes because 60 x (2 / 3) = 40. It takes him 130 minutes in total because 90 + 40 = 130. The answer is 130.

Question: A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?
Answer:
If 1 / 10 of the man's lot is equal to $460, then the man's land is worth $460 x 10 = $4600. Since 1 / 2 of the whole lot is worth $4600, then the whole lot is worth $4600 x 2 = $9200. The answer is 9200.