Half the floors are full, so there are 12 floors * 0.5 = 6 floors that are full. So the full floors contain 6 floors * 10 apartments = 60 apartments. The remaining floors are at half - capacity, so there are 12 floors – 6 full floors = 6 half - full floors. Each of these floors therefore contains 10 apartments * 0.5 = 5 apartments. So on the half - full floors, there are a total of 6 floors * 5 apartments = 30 apartments. In total, there are 30 + 60 = 90 filled apartments in the building. This means there are 90 apartments * 4 people per apartment = 360 people in the building.
The answer: 360
Reverse engineering the question: An apartment building has 12 floors and half of them are full. The remaining floors are all at half-capacity. If each floor has 10 apartments and each apartment has four people, how many people are in the building?


Reasoning and answer: June has 30 days, so if they didn't play any songs on weekends, then they played 30 days - 8 days = 22 days. If Vivian played 10 songs each day, the total number of songs she played for the month is 10 songs / day * 22 days = 220 songs. Clara played 2 fewer songs, which is 10 songs / day - 2 songs / day = 8 songs / day. The total number of songs played by Clara for the whole month is 8 songs / day * 22 days = 176 songs. The total played by both is 220 songs + 176 songs = 396 songs.
The answer: 396
What was the question?
Question: Vivian plays 10 Spotify songs every day. Her best friend Clara plays 2 fewer songs each day. If in June they didn't play any song during the weekends only, and there were 8 weekend days in June, what's the total number of songs they both listened to in that month?


Her hair was 24" long and she cut half off so she cut 24 / 2 = 12 inches. Her hair was 24" long and she cut 12" off so she has 24 - 12 = 12 inches left. She has 12" of hair and lets it grow 4 more inches for a total of 12 + 4 = 16 inches. She has 16" and cuts off 2 more inches which leaves her hair 16 - 2 = 14 inches long.
The answer: 14
Reverse engineering the question: Marcia's hair is 24" long at the beginning of the school year. She cuts half of her hair off and lets it grow out 4 more inches. She then cuts off another 2" of hair. How long is her hair?


Reasoning and answer: We are trying to figure out how many times Max won at Mario Kart, so we'll call that number Y. We know the ratio of Chloe’s wins to Max’s wins is 8 / 3, so 8 / 3 = 24 / Y. Next, we will multiply to find the cross - products. 8 x Y = 3 x 24 or 8Y = 72. We want to get figure out Y, so we need to get it by itself by dividing by 8, like this: 8Y / 8 = 72 / 8. Y = 9, so Max won 9 times.
The answer: 9
What was the question?
Question: Chloe and Max played Mario Kart together. The ratio of Chloe’s wins to Max’s wins is 8:3. Chloe won 24 times. How many times did Max win?


She drinks half a container of a 6 serving bottle of iced coffee a day so she drinks 6 / 2 = 3 servings a day. There are 7 days in a week and she needs enough bottles to last for 2 weeks so that's 7 * 2 = 14 days. She drinks 3 servings a day for 14 days so that's 3 * 14 = 42 servings. Each bottle holds 6 servings and she drinks 42 servings in a week so she needs 42 / 6 = 7 bottles. The iced coffee is on sale for $3.00 a bottle and she needs 7 bottles for a total of 3 * 7 = $21.00.
The answer: 21
Reverse engineering the question: Tricia buys large bottles of iced coffee that have 6 servings per container. She drinks half a container a day. The coffee is currently on sale for $3.00 a bottle. How much will it cost her to buy enough bottles to last for 2 weeks?


Quinton had 40 cupcakes - 18 = 22 cupcakes. He then had 22 cupcakes - 16 students = 6 cupcakes. Quinton then gave away 6 - 1 - 1 - 1 - 1 = 2 cupcakes left.
The answer: 2
Reverse engineering the question:
Quinton brought 40 cupcakes to school on his birthday. He gave a cupcake to each of the 18 students in Ms. Delmont's class. He also gave a cupcake to each of the 16 students in Mrs. Donnelly's class. He also gave a cupcake to Ms. Delmont, Mrs. Donnelly, the school nurse, and the school principal. How many cupcakes did he have left over?