[Question]Brittany, Alex, and Jamy all share 600 marbles divided between them in the ratio 3:5:7. If Brittany gives Alex half of her marbles, what's the total number of marbles that Alex has?
[Answer]The total ratio representing the number of marbles is 3 + 5 + 7 = 15. From the ratio, the fraction representing the number of marbles that Brittany has is 3 / 15, which is equal to 3 / 15 * 600 = 120 marbles. Alex has 5 / 15 * 600 = 200 marbles. If Brittany gives half of her marbles to Alex, Alex receives 1 / 2 * 120 = 60 marbles. After receiving 60 marbles from Brittany, Alex has 200 + 60 = 260 marbles. The answer is 260.
Q: Anthony and his friend Leonel read about the importance of keeping pets at home and decided to start adopting cats and dogs from the local rescue center. Anthony has 12 cats and dogs, 2/3 of which are cats. Leonel has half times as many cats as Anthony and seven more dogs than Anthony. How many animals in total do the two have?
A: If Anthony has 12 pets, the number of cats is 2 / 3 * 12 pets = 8 cats. The number of dogs that Anthony have is 12 pets - 8 cats = 4 dogs. Leonel has 1 / 2 * 8 cats = 4 cats. If Leonel has seven more dogs than Anthony, then he has 4 dogs + 7 dogs = 11 dogs. The total number of pets the two have is 11 dogs for Leonel + 4 cats for Leonel + 4 dogs for Anthony + 8 cats for Anthony = 27. The answer is 27.
Question: Marcus takes a deck of standard playing cards and takes out all the face cards and the 8's. Mark picks a card at random and then replaces it 36 times. How many times should he expect to pick a card that's both red and has a number divisible by 3?
Answer: Without the face cards and the 8's, there are 9 cards of each suit. Half these cards are red, and 3 / 9 have numbers divisible by 3, so the odds of drawing a card divisible by 3 are 1 / 3. Multiply the odds of drawing a red card by the odds of drawing a card divisible by 3 to find the odds of both things happening: 1 / 3 * 1 / 2 = 1 / 6. Finally, multiplying the probability of drawing a red / 3 - divisible card by the number of cards Mark draws to find how many he should expect to meet his criteria: 1 / 6 * 36 cards = 6 cards. The answer is 6.
[Question]Jerry mows 8 acres of lawn each week. He mows ¾ of it with a riding mower that can cut 2 acres an hour. He mows the rest with a push mower that can cut 1 acre an hour. How long does Jerry mow each week?
[Answer]Jerry mows 8 acres x ¾ = 6 acres with a riding mower. It will take him 6 acres / 2 each hour = 3 hours. Jerry mows 8 acres – 6 acres mowed with a riding mower = 2 acres with a push mower. It will take him 2 acres x 1 hour = 2 hours. It takes Jerry a total of 3 hours on the riding mower + 2 hours on the push mower = 5 hours. The answer is 5.
Q: James made $4000 in January. The next month he made twice as much. In March, however, James made $2000 less than in February. How much has James made so far this year?
A: In February James made 4000 * 2 = 8000. In March James made 8000 - 2000 = 6000. In total for the year James has made 4000 + 8000 + 6000 = $18000. The answer is 18000.
Question: A used car lot has 24 cars and motorcycles (in total) for sale. A third of the vehicles are motorcycles, and a quarter of the cars have a spare tire included. How many tires are on the used car lot’s vehicles in all?
Answer:
The used car lot has 24 / 3 = 8 motorcycles with 2 tires each. The lot has 24 - 8 = 16 cars for sale. There are 16 / 4 = 4 cars with a spare tire with 5 tires each. The lot has 16 - 4 = 12 cars with 4 tires each. Thus, the used car lot’s vehicles have 8 * 2 + 4 * 5 + 12 * 4 = 16 + 20 + 48 = 84 tires in all. The answer is 84.