Question: Beth is a scuba diver. She is excavating a sunken ship off the coast of a small Caribbean island and she must remain underwater for long periods. Her primary tank, which she wears when she first enters the water, has enough oxygen to allow her to stay underwater for 2 hours. She also has several 1-hour supplemental tanks that she takes with her as well as stores on the ocean floor so she can change tanks underwater without having to come up to the surface. She will need to be underwater for 8 hours. How many supplemental tanks will she need?
Answer: For an 8 - hour dive, she will use her 2 - hour primary tanks and will need supplemental tanks for 8 - 2 = 6 additional hours. Since each supplemental tank holds 1 hour of oxygen, for 6 hours she will need 6 / 1 = 6 supplemental tanks. The answer is 6.
[Question]Alexander draws 9 pictures for an exhibition at a gallery. 5 new galleries also want Alexander to draw for them, so he draws pictures for their exhibitions too. Each of these new galleries receives the same amount of pictures. For each picture, Alexander needs 4 pencils. For each exhibition, he needs another 2 pencils for signing his signature on the pictures. If Alexander uses 88 pencils on drawing and signing his pictures for all of the exhibitions, how many paintings are at each of the 5 new galleries?
[Answer]Alexander has sent pictures to a total of 1 original gallery + 5 new galleries = 6 galleries. For signatures, he has used a total of 6 galleries * 2 pencils per gallery = 12 pencils. So of the pencils that he used, 88 total pencils 12 signature pencils = 76 pencils for drawings. At the first gallery, he used 9 pictures * 4 pencils per picture = 36 pencils. So in the new galleries, he used 76 total pencils for drawings 36 pencils at the first gallery = 40 pencils. The new galleries received a total of 40 pencils / 4 pencils per picture = 10 pictures. As the new galleries all receive equal amounts of pictures, each gallery must have 10 pictures / 5 galleries = 2 pictures per gallery. The answer is 2.
Q: Kayla and Kylie picked 200 apples total. Kayla picked 1/4 of the apples that Kylie picked. How many apples did Kayla pick?
A: Let x be the number of apples Kylie picked. Kayla picked (1 / 4)x apples. 200 = x + (1 / 4)x. 200 = (5 / 4)x. 200(4 / 5) = 160 = x apples. Kayla picked (1 / 4)(160) = 40 apples. The answer is 40.
Question: Cassidy collects movie posters from newly released sci-fi movies. After this summer, she will have six more posters in her collection, making it double the size it was two years ago when she had 14 posters. How many posters does she have now?
Answer: Let C be the number of posters Cassidy has now. After this summer, she will have twice as many posters as when she had 14, so she will have C + 6 = 2 * 14 = 28 posters. Thus, Cassidy has C = 28 - 6 = 22 posters now. The answer is 22.
[Question]Two teams are playing in a stadium with a capacity of 2000 people. The total number of people in the stadium is 3/4 of the total capacity and each person paid $20 in entry fees. What is the difference between the total amount of fees collected when the stadium was 3/4 full and if the stadium would have been full?
[Answer]When the stadium is full, the total fees charged is 2000 * $20 = $40000. When the stadium is 3 / 4 full, the total number of people in is 3 / 4 * 2000 = 1500 people. The total entry fees collected when the stadium is 3 / 4 full is 1500 * $20 = $30000. The difference in the total entry fees when the stadium is full and when it's 3 / 4 full is $40000 - $30000 = $10000. The answer is 10000.
[Question]An old car can drive 8 miles in one hour. After 5 hours of constant driving, the car needs to get cooled down which takes 1 hour. How many miles can this car drive in 13 hours?
[Answer]
In 5 hours the car can drive 8 * 5 = 40 miles. One cycle of driving and pause takes 5 + 1 = 6 hours. In 13 hours this cycle can fit 13 / 6 = 2 full cycles with a remainder of 1 hour. Two cycles will last for 2 * 6 = 12 hours. During two full cycles, the car will drive 40 * 2 = 80 miles. So there is 13 - 12 = 1 remaining hour when the car can drive. That means during 13 hours the car will be able to drive 80 + 8 = 88 miles. The answer is 88.